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Study of the critical properties of the Quantum Hall Fluid in the framework of a dual statistical model ; By using Renormalization Group methods we analyze the description of the Quantum Hall Fluid in terms of a dual plasma with dyons as effective degrees of freedom. The physical interpretation of the parameters of the model as the longitudinal and Hall conductance togheter with their scaling properties allow for the determination of the critical index. The universality of the critical properties result as a consequence of the generalized duality symmetry of the model.

Semiclassical description of Heisenberg models via spincoherent states ; We use spincoherent states as a timedependent variational ansatz for a semiclassical description of a large family of Heisenberg models. In addition to common approaches we also evaluate the square variance of the Hamiltonian in terms of coherent states. This quantity turns out to have a natural interpretation with respect to timedependent solutions of the equations of motion and allows for an estimate of quantum fluctuations in a semiclassical regime. The general results are applied to solitons, instantons and vortices in several one and twodimensional models.

Spin32 models on the Cayley tree optimum ground state approach ; We present a class of optimum ground states for spin32 models on the Cayley tree with coordination number 3. The interaction is restricted to nearest neighbours and contains 5 continuous parameters. For all values of these parameters the Hamiltonian has parity invariance, spinflip invariance, and rotational symmetry in the xyplane of spin space. The global ground states are constructed in terms of a 1parametric vertex state model, which is a direct generalization of the wellknown matrix product ground state approach. By using recursion relations and the transfer matrix technique we derive exact analytical expressions for local fluctuations and longitudinal and transversal twopoint correlation functions.

Analyticity in Hubbard models ; The Hubbard model describes a lattice system of quantum particles with local onsite interactions. Its free energy is analytic when beta t is small, or beta t2U is small; here, beta is the inverse temperature, U the onsite repulsion and t the hopping coefficient. For more general models with Hamiltonian H V T where V involves local terms only, the free energy is analytic when beta T is small, irrespectively of V. The Gibbs state exists in the thermodynamic limit, is exponentially clustering and thermodynamically stable. These properties are rigorously established in this paper.

Lax pair formulation for a smallpolaron chain with integrable boundaries ; Using a fermionic version of the Lax pair formulation, we construct an integrable smallpolaron model with general open boundary conditions. The Lax pair and the boundary supermatrices Kpm for the model are obtained. This provides a direct proof of the integrability of the model.

The RKKY interactions and the Mott Transition ; A twosite cluster generalization of the Hubbard model in large dimensions is examined in order to study the role of shortrange spin correlations near the metalinsulator transition MIT. The model is mapped to a twoimpurity KondoAnderson model in a selfconsistently determined bath, making it possible to directly address the competition between the Kondo effect and RKKY interactions in a lattice context. Our results indicate that the RKKY interactions lead to qualitative modifications of the MIT scenario even in the absence of long range antiferromagnetic ordering.

Algebraic properties of an integrable tJ model with impurities ; We investigate the algebraic structure of a recently proposed integrable tJ model with impurities. Three forms of the Bethe ansatz equations are presented corresponding to the three choices for the grading. We prove that the Bethe ansatz states are highest weight vectors of the underlying gl21 supersymmetry algebra. By acting with the gl21 generators we construct a complete set of states for the model.

Correlations of Eigenvectors for NonHermitian RandomMatrix Models ; We establish a general relation between the diagonal correlator of eigenvectors and the spectral Green's function for nonhermitian randommatrix models in the largeN limit. We apply this result to a number of nonhermitian randommatrix models and show that the outcome is in good agreement with numerical results.

Exact Solution of a Vertex Model with Unlimited Number of States Per Bond ; The exact solution is obtained for the eigenvalues and eigenvectors of the rowtorow transfer matrix of a twodimensional vertex model with unlimited number of states per bond. This model is a classical counterpart of a quantum spin chain with an unlimited value of spin. This quantum chain is studied using general predictions of conformal field theory. The longdistance behaviour of some groundstate correlation functions is derived from a finitesize analysis of the gapless excitations.

Spread option and exchange option with stochastic interest rates ; In this work, we consider the issue of pricing exchange options and spread options with stochastic interest rates. We provide the closed form solution for the exchange option price when interest rate is stochastic. Our result holds when interest rate is modeled with a stochastic term structure of general form, which includes Vasicek model, CIR term structure, and other wellknown term structure models as special cases. In particular, we have discussed the possibility of using our closed form solution as a control variate in pricing spread options with stochastic interest rate.

Orbital order out of spin disorder How to measure the orbital gap ; The interplay between spin and orbital degrees of freedom in the MottHubbard insulator is studied by considering an orbitally degenerate superexchange model. We argue that orbital order and the orbital excitation gap in this model are generated through the orderfromdisorder mechanism known previously from frustrated spin models. We propose that the orbital gap should show up indirectly in the dynamical spin structure factor; it can therefore be measured using the conventional inelastic neutron scattering method.

A simple solidonsolid model of epitaxial thin films growth surface morphology anisotropy ; In this paper we present a generalization of a simple solidonsolid epitaxial model of thin films growth, when surface morphology anisotropy is provoked by anisotropy in model control parameters binding energy andor diffusion barrier. The anisotropy is discussed in terms of the heightheight correlation function. It was experimentally confirmed that the difference in diffusion barriers yields anisotropy in morphology of the surface. We got antisymmetric correlations in the two inplane directions for antisymmetric binding.

Quantitative Model of Large Magnetostrain Effect in Ferromagnetic Shape Memory Alloys ; A quantitative model describing large magnetostrain effect observed in several ferromagnetic shape memory alloys such as Ni2MnGa is briefly reported.The paper contains an exact thermodynamic consideration of the mechanical and magnetic properties for a similar type materials. As a result, the basic mechanical state equation including magnetic field effect is directly derived from a general Poisson's rule. It is shown that the magnetic field induced deformation effect is directly connected with the strain dependence of magnetization. A simple model of magnetization and its dependence on the strain is considered and applied to explain the results of experimental study of large magnetostrain effects in Ni2MnGa.

A generalization of the spherical model Reentrant phase transition in the spin one ferromagnet ; By mapping the hamiltonian of the spin one ferromagnet onto that of the classical spherical model we investigate the possible phase transitions and the phase diagram of the spin one ferromagnet. Similarly to what happens in the spherical model we find no phase transition in one and two dimensions. Nonetheless, for three dimensions we obtain a phase diagram in which the most important and unexpected feature is the existence of a ferromagneticparamagnetic transition at low temperatures.

Exactly solvable quantum spin tubes and ladders ; We find families of integrable nleg spin12 ladders and tubes with general isotropic exchange interactions between spins. These models are equivalent to suN spin chains with N2n. Arbitrary rung interactions in the spin tubes and ladders induce chemical potentials in the equivalent spin chains. The potentials are ndependent and differ for the tube and ladder models. The models are solvable by means of nested Bethe Ansatz.

On the relation between the anyon and Calogero models ; In order to achieve a dimensional reduction from dimension two to one not only in phase space but also in configuration space, the lowest Landau level LLL projection is not sufficient. One has also, in the LLL, to take the vanishing magnetic field limit, a procedure which can be given a non ambiguous meaning by means of a long distance regulator. As an illustration, the equivalence of the LLL anyon model in the vanishing magnetic field limit to the Calogero model is established. A thermodynamical argument is proposed which supports this claim. Some general considerations in favor of an intimate connexion between anyon and Haldane statistics are also given.

Multiplicity of species in some replicative systems ; In an attempt to explain the uniqueness of the coding mechanism of living cells as contrasted with multispecies structure of ecosystems we examine two models of individuals with some replicative properties. In the first model the system generically remains in a multispecies state. Even though for some of these species the replicative probability is very high, they are unable to invade the system. In the second model, in which the death rate depends on the type of the species, the system relatively quickly reaches a singlespecies state and fluctuations might at most bring it to yet another singlespecies state.

Hole dynamics and photoemission in a tJ model for SrCu2BO32 ; The motion of a single hole in a tJ model for the twodimensional spingap compound SrCu2BO32 is investigated. The undoped Heisenberg model for this system has an exact dimer eigenstate and shows a phase transition between a dimerized and a Neel phase at a certain ratio of the magnetic couplings. We calculate the photoemission spectrum in the disordered phase using a generalized spinpolaron picture. By varying the interdimer hopping parameters we find a crossover between a narrow quasiparticle band regime known from other strongly correlated systems and freefermion behavior. The hole motion in the Neelordered phase is also briefly considered.

Segregation and chargedensitywave order in the spinless FalicovKimball model ; The spinless FalicovKimball model is solved exactly in the limit of infinitedimensions on both the hypercubic and Bethe lattices. The competition between segregation, which is present for large U, and chargedensitywave order, which is prevalent at moderate U, is examined in detail. We find a rich phase diagram which displays both of these phases. The model also shows nonanalytic behavior in the chargedensitywave transition temperature when U is large enough to generate a correlationinduced gap in the singleparticle density of states.

Avalanches at rough surfaces ; We describe the surface properties of a simple lattice model of a sandpile that includes evolving structural disorder. We present a dynamical scaling hypothesis for generic sandpile automata, and additionally explore the kinetic roughening of the sandpile surface, indicating its relationship with the sandpile evolution. Finally, we comment on the surprisingly good agreement found between this model, and a previous continuum model of sandpile dynamics, from the viewpoint of critical phenomena.

A planar diagram approach to the correlation problem ; We transpose an idea of 't Hooft from its context of Yang and Mills' theory of strongly interacting quarks to that of strongly correlated electrons in transition metal oxides and show that a Hubbard model of N interacting electron species reduces, to leading orders in N, to a sum of almost planar diagrams. The resulting generating functional and integral equations are very similar to those of the FLEX approximation of Bickers and Scalapino. This adds the Hubbard model at large N to the list of solvable models of strongly correlated electrons. PACS Numbers 71.27.a 71.10.w 71.10.Fd

Exact Potts Model Partition Functions on Ladder Graphs ; We present exact calculations of the partition function Z of the qstate Potts model and its generalization to real q, the random cluster model, for arbitrary temperature on nvertex ladder graphs with free, cyclic, and Mobius longitudinal boundary conditions. These partition functions are equivalent to TutteWhitney polynomials for these graphs. The free energy is calculated exactly for the infinitelength limit of these ladder graphs and the thermodynamics is discussed.

Microscopic Scenario for Striped Superconductors ; We argue that the superconducting state found in highTc cuprates is inhomogeneous with a corresponding inhomogeneous superfluid density. We introduce two classes of microscopic models which capture the magnetic and superconducting properties of these strongly correlated materials. We start from a generalized tJ model, in which appropriate inhomogeneous terms mimic stripes. We find that inhomogeneous interactions that break magnetic symmetries are essential to induce substantial pair binding of holes in the thermodynamic limit. We argue that this type of model reproduces the ARPES and neutron scattering data seen experimentally.

The Numerical Renormalization Group Method for correlated electrons ; The Numerical Renormalization Group method NRG has been developed by Wilson in the 1970's to investigate the Kondo problem. The NRG allows the nonperturbative calculation of static and dynamic properties for a variety of impurity models. In addition, this method has been recently generalized to lattice models within the Dynamical Mean Field Theory. This paper gives a brief historical overview of the development of the NRG and discusses its application to the Hubbard model; in particular the results for the Mott metalinsulator transition at low temperatures.

Generating moment equations in the Doi model of liquidcrystalline polymers ; We present a selfconsistent method for deriving moment equations for kinetic models of polymer dynamics. The Doi model M. Doi, J.Polymer. Sci., Polym. Phys. Ed. 19, 229 1981 of liquidcrystalline polymers with the Onsager excludedvolume potential is considered as an example. To lowest order, this method amounts to a simple effective potential different from the MaierSaupe form. Analytical results are presented which indicate that this effective potential provides a better approximation to the Onsager potential than the MaierSaupe potential. Corrections to the effective potential are obtained.

LinkedCluster Expansion of the Ising Model ; The linkedcluster expansion technique for the hightemperature expansion of spin model is reviewed. A new algorithm for the computation of threepoint and higher Green's functions is presented. Series are computed for all components of twopoint Green's functions for a generalized 3D Ising model, to 25th order on the bcc lattice and to 23rd order on the sc lattice. Series for zeromomentum four, six, and eightpoint functions are computed to 21st, 19th, and 17th order respectively on the bcc lattice.

Slaveboson meanfield theory of spin and orbitalordered states in the degenerate Hubbard model ; The meanfield theory with the use of the slaveboson functional method is generalized to take account of the spin and orbitalordered state in the doubly degenerate Hubbard model. Some numerical calculations are presented of the antiferromagnetic orbitalordered state in the halffilled simplecubic model. The orbital order in the present theory is much reduced compared with that in the HartreeFock approximation because of the large orbital fluctuations. From a comparison of the groundstate energy, the antiferromagnetic orbital state is shown to be unstable against the antiferromagnetic spin state, although the situation becomes reversed when the exchange interaction is it negative.

YangLee and Fisher Zeros of Multisite Interaction Ising Models on the Cayleytype Lattices ; A general analytical formula for recurrence relations of multisite interaction Ising models in an external magnetic field on the Cayleytype lattices is derived. Using the theory of complex analytical dynamics on the Riemann sphere, a numerical algorithm to obtain YangLee and Fisher zeros of the models is developed. It is shown that the sets of YangLee and Fisher zeros are almost always fractals, that could be associated with Mandelbrotlike sets on the complex magnetic field and temperature planes respectively.

ChapmanEnskog method and synchronization of globally coupled oscillators ; The ChapmanEnskog method of kinetic theory is applied to two problems of synchronization of globally coupled phase oscillators. First, a modified Kuramoto model is obtained in the limit of small inertia from a more general model which includes inertial'' effects. Second, a modified ChapmanEnskog method is used to derive the amplitude equation for an O2 TakensBogdanov bifurcation corresponding to the tricritical point of the Kuramoto model with a bimodal distribution of oscillator natural frequencies. This latter calculation shows that the ChapmanEnskog method is a convenient alternative to normal form calculations.

The Revised Quantum Mechanical Theory of the Optical Activity of Crystals ; In this paper we present the revised view on the optical activity of crystals based on the model of two dumped coupled oscillators. The results are compared with the results of the same problem solved before and it is presented that the results of the quantum mechanical model are the generalization of the classical model only and they do not introduce the new terms of quantum mechanical nature. The results are discussed with regard to the rotational strengths of normal modes of vibrations and the formula for the complex rotatory power containing the rotational strengths is presented.

Diffusion at constant speed in a model phase space ; We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media d1, where the particle can move along 2d directions. We derive the equations for the probability density function using the formulae of differentiation'' of Shapiro and Loginov. The model is an advancement over similiar models of photon migration in multiply scattering media in that it results in a true diffusion at constant speed in the limit of large dimensions.

Normal State Properties of Cuprates tJ Model vs. Experiment ; We discuss some recent results for the properties of doped antiferromagnets, obtained within the planar tJ model mainly by the finitetemperature Lanczos method, with the emphasis on the comparison with experimental results in cuprates. Among the thermodynamic properties the chemical potential and entropy are considered, as well as their relation to the thermoelectric power. At the intermediate doping model results for the optical conductivity, the dynamical spin structure factor and spectral functions reveal a marginal Fermiliquid behaviour, close to experimental findings. It is shown that the universal form of the optical conductivity follows quite generally from the overdamped character of singleparticle excitations.

Small Numerators Canceling Small Denominators Is Dyson's Hierarchical Model Solvable ; We present an analytical method to solve Dyson's hierarchical model, involving the scaling variables near the hightemperature fixed point. The procedure seems plagued by the presence of small denominators as in perturbative expansions near integrable systems in Hamiltonian mechanics. However, in all cases considered, a zero denominator always comes with a zero numerator. We conjecture that these cancellations occur in general, suggesting that the model has remarkable features reminiscent of the integrable systems.

Driven diffusive system A study on large n limit ; We study the generalized n component model of a driven diffusive system with annealed random drive in the large n limit. This nonequilibrium model also describes conserved order parameter dynamics of an equilibrium model of ferromagnets with dipolar interaction. In this limit, at zero temperature a saddle point approximation becomes exact. The length scale in the direction transverse to the driving field acquires an additional logarithmic correction in this limit.

A model for the atomicscale structure of a dense, nonequilibrium fluid the homogeneous cooling state of granular fluids ; It is shown that the equilibrium Generalized Mean Spherical Model of fluid structure may be extended to nonequilibrium states with equation of state information used in equilibrium replaced by an exact condition on the twobody distribution function. The model is applied to the homogeneous cooling state of granular fluids and upon comparison to molecular dynamics simulations is found to provide an accurate picture of the pair distribution function.

Kinetics of Coalescence, Annihilation, and the qState Potts Model in One Dimension ; The kinetics of the qstate Potts model in the zero temperature limit in one dimension is analyzed exactly through a generalization of the method of empty intervals, previously used for the analysis of diffusionlimited coalescence, AAA. In this new approach, the qstate Potts model, coalescence, and annihilation AA0 all satisfy the same diffusion equation, and differ only in the imposed initial condition.

Exactly Solvable Single Lane Highway Traffic Model With Tollbooths ; Tolls are collected on many highways as a means of traffic control and revenue generation. However, the presence of tollbooths on highway surely slows down traffic flow. Here, we investigate how the presence of tollbooths affect the average car speed using a simpleminded single lane deterministic discrete traffic model. More importantly, the model is exactly solvable.

Dichromatic polynomials and Potts models summed over rooted maps ; We consider the sum of dichromatic polynomials over nonseparable rooted planar maps, an interesting special case of which is the enumeration of such maps. We present some known results and derive new ones. The general problem is equivalent to the qstate Potts model randomized over such maps. Like the regular ferromagnetic lattice models, it has a firstorder transition when q is greater than a critical value qc, but qc is much larger about 72 instead of 4.

On a universal mechanism for long ranged volatility correlations ; We propose a general interpretation for longrange correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between active' and inactive' strategies is subordinated to randomwalk like processes. We numerically demonstrate our scenario in the framework of simplified market models, such as the Minority Game model with an inactive strategy. We show that real market data can be surprisingly well accounted for by these simple models.

The excitations of the sympletic integrable models and their applications ; The Bethe ansatz equations of the fundamental Sp2N integrable model are solved by a peculiar configuration of roots leading us to determine the nature of the excitations. They consist of N elementary generalized spinons and N1 composite excitations made by special convolutions between the spinons. This fact is essential to determine the lowenergy behaviour which is argued to be described in terms of 2N Majorana fermions. Our results have practical applications to spinorbital systems and also shed new light to the connection between integrable models and WessZuminoWitten field theories.

Selfduality in MaxwellChernSimons theories with non minimal coupling with field ; We consider a general class of nonlocal MCS models whose usual minimal coupling to a conserved current is supplemented with a nonminimal magnetic Paulitype coupling. We find that the considered models exhibit a selfduality whenever the magnetic coupling constant reaches a special value the partition function is invariant under a set of transformations among the parameter space the duality transformations while the original action and its dual counterpart have the same form. The duality transformations have a structure similar to the one underlying selfduality of the 21dimensional Znabelian Higgs model with ChernSimons and bare mass term.

Thermal Reemission Model ; Starting from a continuum description, we study the nonequilibrium roughening of a thermal reemission model for etching in one and two spatial dimensions. Using standard analytical techniques, we map our problem to a generalized version of an earlier nonlocal KPZ KardarParisiZhang model. In 21 dimensions, the values of the roughness and the dynamic exponents calculated from our theory go like alpha approx z approx 1 and in 11 dimensions, the exponents resemble the KPZ values for low vapor pressure, supporting experimental results. Interestingly, Galilean invariance is maintained althrough.

Inherent Structures in models for fragile and strong glass ; An analysis of the dynamics is performed, of exactly solvable models for fragile and strong glasses, exploiting the partitioning of the free energy landscape in inherent structures. The results are compared with the exact solution of the dynamics, by employing the formulation of an effective temperature used in literature. Also a new formulation is introduced, based upon general statistical considerations, that performs better. Though the considered models are conceptually simple there is no limit in which the inherent structure approach is exact.

Transport coefficients at Metastable Densities from models of Generalized Hydrodynamics ; In the present work we compute the enhancement in the long time transport coefficients due to correlated motion of fluid particles at high density. The fully wave vecor dependent extended mode coupling model is studied with the inclusion of an additional slow variable of the defect density for the amorphous system. We use the extremely slow relaxation of the density correlation function observed in the light scattering experiments on colloids to estimate the input parameters for the model The ratio of long time to short time diffusion coefficient is studied around the the peak of the structure factor.

Defensive alliances in spatial models of cyclical population interactions ; As a generalization of the 3strategy RockScissorsPaper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated and a neutral interacting partner. Depending on their interaction topologies, these systems can be classified into four isomorphic groups exhibiting significantly different behaviors as a function of mutation rate. On three out of four cases three or four species form defensive alliances which maintain themselves in a selforganizing polydomain structure via cyclic invasions. Varying the mutation rate this mechanism results in an ordering phenomenon analogous to that of magnetic Ising model.

Exactly solvable models through the empty interval method ; The most general one dimensional reactiondiffusion model with nearestneighbor interactions, which is exactlysolvable through the empty interval method, has been introduced. Assuming translationallyinvariant initial conditions, the probability that n consecutive sites are empty En, has been exactly obtained. In the thermodynamic limit, the largetime behavior of the system has also been investigated. Releasing the translational invariance of the initial conditions, the evolution equation for the probability that n consecutive sites, starting from the site k, are empty Ek,n is obtained. In the thermodynamic limit, the large time behavior of the system is also considered. Finally, the continuum limit of the model is considered, and the emptyinterval probability function is obtained.

Designability of lattice model heteropolymers ; Protein folds are highly designable, in the sense that many sequences fold to the same conformation. In the present work we derive an expression for the designability in a 20 letter lattice model of proteins which, relying only on the Central Limit Theorem, has a generality which goes beyond the simple model used in its derivation. This expression displays an exponential dependence on the energy of the optimal sequence folding on the given conformation measured with respect to the lowest energy of the conformational dissimilar structures, energy difference which constitutes the only parameter controlling designability. Accordingly, the designability of a native conformation is intimately connected to the stability of the sequences folding to them.

Random phase approximation for multiband Hubbard models ; We derive the randomphase approximation for spin excitations in general multiband Hubbard models, starting from a collinear ferromagnetic HartreeFock ground state. The results are compared with those of a recently introduced variational manybody approach to spinwaves in itinerant ferromagnets. As we exemplify for Hubbard models with one and two bands, the two approaches lead to qualitatively different results. The discrepancies can be traced back to the fact that the HartreeFock theory fails to describe properly the local moments which naturally arise in a correlatedelectron theory.

Quantum Heisenberg Antiferromagnets versus Nonlinear Model Without the Large S Limit ; In this letter, I develop a new topologically invariant coherent state path integral for spin systems, and apply it to the quantum Heisenberg model on a square lattice. As a result, the quantum nonlinear sigma model for arbitrary values of spin can be directly obtained. The effective coupling constant and spin wave velocity are modified by gs 2over SsqrtdTLambdaover 2SJ and cs2JSa sqrtdTLambdaover 2SJ, where TLambda is a natural temperature scale for the reliability of the theory. The formulation can also be extended to other generalized coherent state path integrals.

Memory effects in vibrated granular systems ; Granular materials present memory effects when submitted to tapping processes. These effects have been observed experimentally and are discussed here in the context of a general kind of model systems for compaction formulated at a mesoscopic level. The theoretical predictions qualitatively agree with the experimental results. As an example, a particular simple model is used for detailed calculations.

Percolation and epidemics in a twodimensional small world ; Percolation on twodimensional smallworld networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and highorder series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of shortcuts in the smallworld network. Our results agree with scaling hypotheses and numerical simulations for the same model.

Hopping models and ac universality ; Some general relations for hopping models are established. We proceed to discuss the universality of the ac conductivity which arises in the extreme disorder limit of the random barrier model. It is shown that the relevant dimension entering into the diffusion cluster approximation DCA is the harmonic fracton dimension of the diffusion cluster. The temperature scaling of the dimensionless frequency entering into the DCA is discussed. Finally, some open questions about ac universality are mentioned.

Nonequilibrium Phase Transitions in Epidemics and Sandpiles ; Nonequilibrium phase transitions between an active and an absorbing state are found in models of populations, epidemics, autocatalysis, and chemical reactions on a surface. While absorbingstate phase transitions fall generically in the DP universality class, this does not preclude other universality classes, associated with a symmetry or conservation law. An interesting issue concerns the dynamic critical behavior of models with an infinite number of absorbing configurations or a long memory. Sandpile models, the principal example of selforganized criticality SOC, also exhibit absorbing state phase transitions, with SOC corresponding to a particular mode of forcing the system toward its critical point.

Growing ScaleFree Networks with Tunable Clustering ; We extend the standard scalefree network model to include a triad formation step''. We analyze the geometric properties of networks generated by this algorithm both analytically and by numerical calculations, and find that our model possesses the same characteristics as the standard scalefree networks like the powerlaw degree distribution and the small average geodesic length, but with the highclustering at the same time. In our model, the clustering coefficient is also shown to be tunable simply by changing a control parameter the average number of triad formation trials per time step.

Exact solutions of epidemic models on networks ; The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the socalled susceptibleinfectiveremoved models, and many of their generalizations, can be solved exactly on a wide variety of networks. Solutions are possible for cases with heterogeneous or correlated probabilities of transmission, cases incorporating vaccination, and cases in which the network has complex structure of various kinds. We confirm the correctness of our solutions by comparison with computer simulations of epidemics propagating on the corresponding networks.

Hierarchical Random Telegraph Signals in nanojunctions with Coulomb correlations ; We propose a microscopic hamiltonian together with a master equation description to model stochastic hierarchical Random Telegraph Signal RTS or Popcorn noise in nanojunctions. The microscopic model incorporates the crucial Coulomb correlations due to the trapped charges inside the junction or at the metaloxide interface. The exact solution of the microscopic model is based on a generalization of the NozieresDe Dominicis method devised to treat the problem of the edge singularity in the Xray absorption and emission spectra of metals. In the master equation description, the experimentally accessible transition rates are expressed in terms of the exact multichannel Scattering matrix of the microscopic hamiltonian.

Quantum dimer model on the kagome lattice solvable dimer liquid and Ising gauge theory ; We introduce quantum dimer models on lattices made of cornersharing triangles. These lattices includes the kagome lattice and can be defined in arbitrary geometry. They realize fully disordered and gapped dimerliquid phase with topological degeneracy and deconfined fractional excitations, as well as solid phases. Using geometrical properties of the lattice, several results are obtained exactly, including the full spectrum of a dimerliquid. These models offer a very natural and maybe the simplest possible framework to illustrate general concepts such as fractionalization, topological order and relation to Z2 gauge theories.

New series of integrable vertex models through a unifying approach ; Applying a unifying Lax operator approach to statistical systems a new class of integrable vertex models based on quantum algebra is proposed, which exhibits a rich variety for generic q, q roots of unity and q 1. Exact solutions are formulated through algebraic Bethe ansatz and a novel possibility of hybrid vertex models is introduced.

Exact Solution of the MunozEaton Model for Protein Folding ; A transfermatrix formalism is introduced to evaluate exactly the partition function of the MunozEaton model, relating the folding kinetics of proteins of known structure to their thermodynamics and topology. This technique can be used for a generic protein, for any choice of the energy and entropy parameters, and in principle allows the model to be used as a first tool to characterize the dynamics of a protein of known native state and equilibrium population. Applications to a betahairpin and to protein CI2, with comparisons to previous results, are also shown.

High temperature superconductivity in dimer array systems ; Superconductivity in the Hubbard model is studied on a series of lattices in which dimers are coupled in various types of arrays. Using fluctuation exchange method and solving the linearized Eliashberg equation, the transition temperature Tc of these systems is estimated to be much higher than that of the Hubbard model on a simple square lattice, which is a model for the high Tc cuprates. We conclude that these dimer array' systems can generally exhibit superconductivity with very high Tc. Not only delectron systems, but also pelectron systems may provide various stages for realizing the present mechanism.

Ultrametricity Between States at Different Temperatures in SpinGlasses ; We prove the existence of correlations between the equilibrium states at different temperatures of the multipspin spherical spinglass models with continuous replica symmetry breaking there is no chaos in temperature in these models. Furthermore, the overlaps satisfy ultrametric relations. As a consequence the Parisi tree is essentially the same at all temperatures with lower branches developing when lowering the temperature. We conjecture that the reference free energies of the clusters are also fixed at all temperatures as in the generalized randomenergy model.

Existence of a New Quantum Phase in Exactly Solvable Antiferromagnetic IsingHeisenberg Models on Planar Lattices ; In this work we deal with doubly decorated IsingHeisenberg models on planar lattices. Applying the generalized decorationiteration transformation we obtain exact results for the antiferromagnetic version of the model. The existence of a new quantum dimerized phase is predicted and its physical properties are studied and analyzed. Particular attention has been paid to the investigation of the phase boundaries, paircorrelation functions and specific heat. A possible application of the present work to some molecular magnets is also drawn.

Thermodynamic properties of the exactly solvable transverse Ising model on decorated planar lattices ; The generalized mapping transformation technique is used to obtain the exact solution for the transverse Ising model on decorated planar lattices. Within this scheme, the basic thermodynamic quantities are calculated for different planar lattices with arbitrary spins of decorating atoms. The particular attention has been paid to the investigation of the transversefield effects on magnetic properties of the system under investigation. The most interesting numerical results for the phase diagrams, compensation temperatures and several thermodynamic quantities are discussed in detail for the ferrimagnetic version of the model.

Magnetic properties of superconducting multifilamentary tapes in perpendicular field. I Model and vertical stacks ; Current and field profiles, and magnetization and AC losses are calculated for an array of infinitely long superconducting tapes arranged vertically in a perpendicularly applied magnetic field. Calculations are based on the critical state model. The finite thickness of the tapes and the effects of demagnetizing fields are considered. The influence of the magnetic coupling of the filaments in the magnetic properties of the arrays are studied. The general model can be applied to an arbitrary arrangement of tapes as long as there is reflection symmetry with respect to the vertical central plane.

Singleparticle dynamics of the Anderson model a local moment approach ; A nonperturbative local moment approach to singleparticle dynamics of the general asymmetric Anderson impurity model is developed. The approach encompasses all energy scales and interaction strengths. It captures thereby strong coupling Kondo behaviour, including the resultant universal scaling behaviour of the singleparticle spectrum; as well as the mixed valent and essentially perturbative empty orbital regimes. The underlying approach is physically transparent and innately simple, and as such is capable of practical extension to latticebased models within the framework of dynamical meanfield theory.

Dynamical model of financial markets fluctuating temperature' causes intermittent behavior of price changes ; We present a model of financial markets originally proposed for a turbulent flow, as a dynamic basis of its intermittent behavior. Time evolution of the price change is assumed to be described by Brownian motion in a powerlaw potential, where the temperature' fluctuates slowly. The model generally yields a fattailed distribution of the price change. Specifically a Tsallis distribution is obtained if the inverse temperature is chi2distributed, which qualitatively agrees with intraday data of foreign exchange market. The socalled volatility', a quantity indicating the risk or activity in financial markets, corresponds to the temperature of markets and its fluctuation leads to intermittency.

How effective is advertising in duopoly markets ; A simple Ising spin model which can describe the mechanism of advertising in a duopoly market is proposed. In contrast to other agentbased models, the influence does not flow inward from the surrounding neighbors to the center site, but spreads outward from the center to the neighbors. The model thus describes the spread of opinions among customers. It is shown via standard Monte Carlo simulations that very simple rules and inclusion of an external field an advertising campaign lead to phase transitions.

Einstein Relation for Nonequilibrium Steady States ; The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds if the steady state satisfies detailed balance. More generally, we consider nonequilibrium steady states where detailed balance does not hold and show how a generalisation of the Einstein relation may be derived in certain cases. In particular, for the asymmetric simple exclusion process and a driven diffusive dimer model, the external perturbation creates and annihilates particles thus breaking the particle conservation of the unperturbed model.

Avalanche exponents and corrections to scaling for a stochastic sandpile ; We study distributions of dissipative and nondissipative avalanches in Manna's stochastic sandpile, in one and two dimensions. Our results lead to the following conclusions 1 avalanche distributions, in general, do not follow simple power laws, but rather have the form Ps sim staus ln sgamma fssc, with f a cutoff function; 2 the exponents for sizes of dissipative avalanches in two dimensions differ markedly from the corresponding values for the BakTangWiesenfeld BTW model, implying that the BTW and Manna models belong to distinct universality classes; 3 dissipative avalanche distributions obey finite size scaling, unlike in the BTW model.

A hybrid model for chaotic front dynamics From semiconductors to water tanks ; We present a general method for studying front propagation in nonlinear systems with a global constraint in the language of hybrid tank models. The method is illustrated in the case of semiconductor superlattices, where the dynamics of the electron accumulation and depletion fronts shows complex spatiotemporal patterns, including chaos. We show that this behavior may be elegantly explained by a tank model, for which analytical results on the emergence of chaos are available. In particular, for the case of three tanks the bifurcation scenario is characterized by a modified version of the onedimensional iterated tentmap.

Assisted hopping in the Anderson impurity model A flow equation study ; We investigate the effect of assisted hopping in the Anderson impurity model. We use the flow equation method, which, by means of unitary transformations, generates a sequence of Hamiltonians in order to eliminate the assisted hopping terms. This approach yields a renormalized onsite energy epsilond, a renormalized correlation energy U and other terms, which include pair hopping. For some parameter values, the initial Hamiltonian flows towards an attractive Anderson model. We argue that this result implies a tendency towards local pairing fluctuations.

Model of Controlled Synthesis of Uniform Colloid Particles Cadmium Sulfide ; The recently developed twostage growth model of synthesis of monodispersed polycrystalline colloidal particles is utilized and improved to explain growth of uniform cadmium sulfide spheres. The model accounts for the coupled processes of nucleation, which yields nanocrystalline precursors, and aggregation of these subunits to form the final particles. The key parameters have been identified that control the size selection and uniformity of the CdS spheres, as well as the dynamics of the process. This approach can be used to generally describe the formation of monodispersed colloids by precipitation from homogeneous solutions.

A foodweb based unified model of macro and micro evolution ; We incorporate the generic hierarchical architecture of foodwebs into a it unified model that describes both micro and macro evolutions within a single theoretical framework. This model describes the micro evolution in detail by accounting for the birth, ageing and natural death of individual organisms as well as preypredator interactions on a hierarchical dynamic food web. It also provides a natural description of random mutations and speciationorgination of species as well as their extinctions. The distribution of lifetimes of species follows an approximate power law only over a limited regime.

Landau Transport equations in slaveboson meanfield theory of tJ model ; In this paper we generalize slaveboson meanfield theory for tJ model to the timedependent regime, and derive transport equations for tJ model, both in the normal and superconducting states. By eliminating the boson and constraint fields exactly in the equations of motion we obtain a set of transport equations for fermions which have the same form as Landau transport equations for normal Fermi liquid and Fermi liquid superconductor, respectively with all Landau parameters explicity given. Our theory can be viewed as a refined version of U1 Gauge theory where all lattice effects are retained and strong correlation effects are reflected as strong Fermiliquid interactions in the transport equation. Some experimental consequences are discussed.

Some New Exact Results for the qState Potts Model on Ladder Graphs ; We present exact calculations of the partition function for the qstate Potts model for general q, temperature and magnetic field on strips of the square lattices of width Ly2 and arbitrary length Lx m with periodic longitudinal boundary conditions. A new representation of the transfer matrix for the qstate Potts model is introduced which can be used to calculate the determinant of the transfer matrix for an arbirary m times m lattice with periodic boundary conditions.

Shedding light on El Farol ; We mathematize El Farol bar problem and transform it into a workable model. In general, the average convergence to optimality at the collective level is trivial and does not even require any intelligence on the side of agents. Secondly, specializing to a particular ensemble of continuous strategies yields a model similar to the Minority Game. Statistical physics of disordered systems allows us to derive a complete understanding of the complex behavior of this model, on the basis of its phase diagram.

Tensorial Constitutive Models for Disordered Foams, Dense Emulsions, and other Soft Nonergodic Materials ; In recent years, the paradigm of soft glassy matter' has been used to describe diverse nonergodic materials exhibiting strong local disorder and slow mesoscopic rearrangement. As so far formulated, however, the resulting soft glassy rheology' SGR model treats the shear stress in isolation, effectively scalarizing' the stress and strain rate tensors. Here we offer generalizations of the SGR model that combine its nontrivial aging and yield properties with a tensorial structure that can be specifically adapted, for example, to the description of fluid film assemblies or disordered foams.

Dynamic Hubbard Model Effect of Finite Boson Frequency ; Dynamic Hubbard models describe coupling of a boson degree of freedom to the onsite electronic double occupancy. In the limit of infinite boson frequency this coupling gives rise to a correlated hopping term in the effective Hamiltonian and to superconductivity when the Fermi level is near the top of the band. Here we study the effect of finite boson frequency through a generalized LangFirsov transformation and a high frequency expansion. It is found that finite frequency enhances the tendency to superconductivity in this model.

Assortative model for social networks ; In this paper we present a new version of a network growth model, generalized in order to describe the behavior of social networks. The case of study considered is the preprint archive at cul.arxiv.org. Each node corresponds to a scientist, and a link is present whenever two authors wrote a paper together. This graph is a nice example of degreeassortative network, that is to say a network where sites with similar degree are connected each other. The model presented is one of the few able to reproduce such behavior, giving some insight on the microscopic dynamics at the basis of the graph structure.

Phase diagram of the frustrated Hubbard model ; The MottHubbard metalinsulator transition in the paramagnetic phase of the oneband Hubbard model has long been used to describe similar features in real materials like V2O3. Here we show that this transition is hidden inside a rather robust antiferromagnetic insulator even in the presence of comparatively strong magnetic frustration. This result raises the question of the relevance of the MottHubbard metalinsulator transition for the generic phase diagram of the oneband Hubbard model.

Semiclassical theory for quantum spin models with ring exchange on the triangular lattice ; A semiclassical theory of a quantum spinS model with competing ring and Heisenberg exchange terms on the triangular lattice is obtained. A mechanism for the generation of Z2 vortices is exhibited. The vortices are shown to carry a nontrivial geometric phase for the order parameter when 2S is odd, leading to a difference between the quantum disordered ground states and low energy spectra for half odd integer and half even integer spin systems, and a topological degeneracy on surfaces with nontrivial cycles. A connection to dimer models is discussed.

Potts model on complex networks ; We consider the general pstate Potts model on random networks with a given degree distribution random Bethe lattices. We find the effect of the suppression of a first order phase transition in this model when the degree distribution of the network is fattailed, that is, in more precise terms, when the second moment of the distribution diverges. In this situation the transition is continuous and of infinite order, and size effect is anomalously strong. In particular, in the case of p1, we arrive at the exact solution, which coincides with the known solution of the percolation problem on these networks.

Memory and Kovacs effects in the parkinglot model an approximate statisticalmechanical treatment ; The parkinglot model provides a qualitative description of the main features of the phenomenology of granular compaction. We derive here approximate kinetic equations for this model, equations that are based on a 2parameter generalization of the statisticalmechanical formalism first proposed by Edwards and coworkers. We show that historydependent effects, such as memory and Kovacs effects, are captured by this approach.

Stochastic energycascade model for 11 dimensional fully developed turbulence ; Geometrical random multiplicative cascade processes are often used to model positivevalued multifractal fields such as the energy dissipation in fully developed turbulence. We propose a dynamical generalization describing the energy dissipation in terms of a continuous and homogeneous stochastic field in one space and one time dimension. In the model, correlations originate in the overlap of the respective spacetime histories of field amplitudes. The theoretical two and threepoint correlation functions are found to be in good agreement with their equaltime counterparts extracted from wind tunnel turbulent shear flow data.

Weighted evolving networks coupling topology and weights dynamics ; We propose a model for the growth of weighted networks that couples the establishment of new edges and vertices and the weights' dynamical evolution. The model is based on a simple weightdriven dynamics and generates networks exhibiting the statistical properties observed in several realworld systems. In particular, the model yields a nontrivial time evolution of vertices' properties and scalefree behavior for the weight, strength and degree distributions.

Critical properties of a continuous family of XY noncollinear magnets ; Monte Carlo methods are used to study a family of three dimensional XY frustrated models interpolating continuously between the stacked triangular antiferromagnets and a variant of this model for which a local rigidity constraint is imposed. Our study leads us to conclude that generically weak first order behavior occurs in this family of models in agreement with a recent nonperturbative renormalization group description of frustrated magnets.

Landau theory of glassy dynamics ; An exact solution of a Landau model of an orderdisorder transition with activated critical dynamics is presented. The model describes a funnelshaped topography of the order parameter space in which the number of energy lowering trajectories rapidly diminishes as the ordered groundstate is approached. This leads to an asymmetry in the effective transition rates which results in a nonexponential relaxation of the orderparameter fluctuations and a VogelFulcherTammann divergence of the relaxation times, typical of a glass transition. We argue that the Landau model provides a general framework for studying glassy dynamics in a variety of systems.

Random MultiOverlap Structures and Cavity Fields in Diluted Spin Glasses ; We introduce the concept of Random MultiOverlap Structures in diluted spin glasses, following the ideas of Aizenman, Sims and Starr for nondiluted models. As a result, we prove the generalized bound and variational principle for the free energy per site, in analogy with the results of Aizenman, Sims and Starr for nondiluted models. We also prove some stability properties of the optimal RMOSt, analogous to the one found by Guerra for nondiluted models.

Exactlysolvable models for atommolecule hamiltonians ; We present a family of exactlysolvable generalizations of the JaynesCummings model involving the interaction of an ensemble of SU2 or SU1,1 quasispins with a single boson field. They are obtained from the trigonometric RichardsonGaudin models by replacing one of the SU2 or SU1,1 degrees of freedom by an ideal boson. Application to a system of bosonic atoms and molecules is reported.

Spins wavefunctions with algebraic order ; We generalize the Gutzwiller wavefunction for s 12 spin chains to construct a family of wavefunctions for all s 12. Through numerical simulations, we demonstrate that the spin spin correlation functions for all s decay as a power law with logarithmic corrections. This is done by mapping the model to a classical statistical mechanical model, which has coupled Ising spin chains with long range interactions. The power law exponents are those of the Wess Zumino Witten models with k 2s. Thus these simple wavefunctions reproduce the spin correlations of the family of Hamiltonians obtained by the Algebraic Bethe Ansatz.

Destruction of the Kondo effect in a multichannel BoseFermi Kondo model ; We consider the SUN x SUkappa N generalization of the spinisotropic BoseFermi Kondo model in the limit of large N. There are three fixed points corresponding to a multichannel nonFermi liquid phase, a local spinliquid phase, and a Kondodestroying quantum critical point QCP. We show that the QCP has strong similarities with its counterpart in the singlechannel model, even though the Kondo phase is very different from the latter. We also discuss the evolution of the dynamical scaling properties away from the QCP.

Subcritical behavior in the alternating supercritical DomanyKinzel dynamics ; Cellular automata are widely used to model realworld dynamics. We show using the DomanyKinzel probabilistic cellular automata that alternating two supercritical dynamics can result in subcritical dynamics in which the population dies out. The analysis of the original and reduced models reveals generality of this paradoxical behavior, which suggests that autonomous or manmade periodic or random environmental changes can cause extinction in otherwise safe population dynamics. Our model also realizes another scenario for the Parrondo's paradox to occur, namely, spatial extensions.

Inclusion of Experimental Information in First Principles Modeling of Materials ; We propose a novel approach to model amorphous materials using a first principles density functional method while simultaneously enforcing agreement with selected experimental data. We illustrate our method with applications to amorphous silicon and glassy GeSe2. The structural, vibrational and electronic properties of the models are found to be in agreement with experimental results. The method is general and can be extended to other complex materials.

Glass transition in models with controlled frustration ; A class of models with selfgenerated disorder and controlled frustration is studied. Between the trivial case, where frustration is not present at all, and the limit case, where frustration is present over every length scale, a region with local frustration is found where glassy dynamics appears. We suggest that in this region, the mean field model might undergo a pspin like transition, and increasing the range of frustration, a crossover from a 1step replica symmetry breaking to a continuous one might be observed.

Drying model for porous material based on the dynamics of the evaporation front ; A recedingfront model for drying of porous material is proposed that explains their dryingrate curves based on the dynamics of the evaporation front. The fallingrate regime is attributed to the slowing down of the front's propagation inside the medium due to the resistance offered by the disorder generated by porosity. The model is solved numerically and the resulting dryingrate curve is obtained for the fallingrate period. The curve shows a linear behavior at early times in conformance with experiment.

A refined RazumovStroganov conjecture II ; We extend a previous conjecture condmat0407477 relating the PerronFrobenius eigenvector of the monodromy matrix of the O1 loop model to refined numbers of alternating sign matrices. By considering the O1 loop model on a semiinfinite cylinder with dislocations, we obtain the generating function for alternating sign matrices with prescribed positions of 1's on their top and bottom rows. This seems to indicate a deep correspondence between observables in both models.

The Exchange Gate in Solid State Spin Quantum Computation The Applicability of the Heisenberg Model ; Solid state quantum computing proposals rely on adiabatic operations of the exchange gate among localized spins in nanostructures. We study corrections to the Heisenberg interaction between lateral semiconductor quantum dots in an external magnetic field. Using exact diagonalization we obtain the regime of validity of the adiabatic approximation. We also find qualitative corrections to the Heisenberg model at high magnetic fields and in looped arrays of spins. Looped geometries of localized spins generate flux dependent, multispin terms which go beyond the basic Heisenberg model.

Twodimensional gapless spin liquids in frustrated SUN quantum magnets ; A class of the symmetrically frustrated SUN models is constructed for quantum magnets based on the generators of SUN group. The total Hamiltonian lacks SUN symmtry. A mean field theory in the quasiparticle representation is developed for spin liquid states. Numerical solutions in two dimension indicate that the ground states are gapless and the quasiparticles are Dirac particles. The mechanism may be helpful in exploring the spin liquid phases in the spin1 bilinearbiquadratic model and the spinorbital model in higher dimensions.

Kondo resonance for orbitally degenerate systems ; Formation of the Kondo state in general twoband Anderson model has been investigated within the numerical renormalization group NRG calculations. The AbrikosovSuhl resonance is essentially asymmetric for the model with one electron per impurity quarter filling case in contrast with the oneband case. An external magnetic pseudomagnetic field breaking spin orbital degeneracy leads to asymmetric splitting and essential broadening of the manybody resonance. Unlike the standard Anderson model, the spin up'' Kondo peak is pinned against the Fermi level, but not suppressed by magnetic field.

Low Temperature Specific Heat of some Quantum Mean Field glassy phases ; We investigate analytically the low temperature behavior of the specific heat CvT for a large class of quantum disordered models within Mean Field approximation. This includes the vibrational modes of a lattice pinned by impurity disorder in the quantum regime, the quantum spherical pspinglass and a quantum Heisenberg spin glass. We exhibit a general mechanism, common to all these models, arising from the socalled marginality condition, responsible for the cancellation of the linear and quadratic contributions in T in the specific heat. We thus find for all these models the Mean Field result CvT propto T3.