16350340
Two Ising models coupled to two-dimensional gravity
Abstract To investigate the properties of c = 1 matter coupled to 2d-gravity we have performed large-scale simulations ot two copies of the Ising model on a dynamical lattice. We measure spin susceptibility and percolation critical exponents using finite-size scaling. We show explicity how algorithmic corrections are needed for a proper comparison with theoretical exponents. We also exhibit correlations, mediated by gravity, between the energy and magnetic properties of the two Ising species. The prospects for extending this work beyond c = 1 are dressed.
119499105
Anisotropic Membranes
We describe the statistical behavior of anisotropic crystalline membranes. In particular we give the phase diagram and critical exponents for phantom membranes and discuss the generalization to self-avoiding membranes.
122263335
Multiple Ising models coupled to 2-d gravity: a CSD analysis
Abstract We simulate single and multiple Ising models coupled to 2-d gravity and we measure critical slowing down (CSD) with the standard methods. We find that the Swendsen-Wang and Wolff cluster algorithms do not eliminate CSD. We interpret the result as an effect of the mesh dynamics.
14633114
The phase diagram of crystalline surfaces
We report the status of a high-statistics Monte Carlo simulation of non-self-avoiding crystalline surfaces with extrinsic curvature on lattices of size up to 128 2 nodes. We impose free boundary conditions. The free energy is a gaussian spring tethering potential together with a normal-normal bending energy. Particular emphasis is given to the behavior of the model in the cold phase where we measure the decay of the normal-normal correlation function.
575888
Fluid random surfaces with extrinsic curvature. II
Abstract We present the results of an extension of our previous work on large-scale simulations of dynamically triangulated toroidal random surfaces embedded in R 3 with extrinsic curvature. We find that the extrinsic-curvature specific heat peak ceases to grow on lattices with more than 576 nodes and that the location of the peak λ c also stabilizes. The evidence for a true crumpling transition is still weak. If we assume it exists we can say that the finite-size scaling exponent α / ηd is very close to zero or negative. On the other hand our new data does rule out the observed peak as being a finite-size artifact of the persistence length becoming comparable to the extent of the lattice.
9011435
Critical slowing down of cluster algorithms for Ising models coupled to 2-d gravity
Abstract We simulate single and multiple Ising models coupled to 2-d gravity using both the Swendsen-Wang and Wolff algorithms to update the spins. We study the integrated autocorrelation time and find that there is considerable critical slowing down, particularly in the magnetization. We argue that this is primarily due to the local nature of the dynamical triangulation algorithm and to the generation of a distribution of baby universes which inhibits cluster growth.
15060511
Transition from regular to complex behaviour in a discrete deterministic asymmetric neural network model
The authors study the long-time behaviour of the transient before the collapse on the periodic attractors of a discrete deterministic asymmetric neural network model. The system has a finite number of possible states so it is not possible to use the term chaos in the usual sense of sensitive dependence on the initial condition. Nevertheless, on varying the asymmetry parameter, k, one observes a transition from ordered motion (i.e. short transients and short periods on the attractors) to 'complex' temporal behaviour. This transition takes place for the same value kc at which one has a change in behaviour for the mean transient length from a power law in the size of the system (N) to an exponential law in N. The 'complex' behaviour during the transient shows strong analogies with chaotic behaviour: decay of temporal correlations, positive Shannon entropy, nonconstant Renyi entropies of different orders. Moreover the transition is very similar to the intermittent transition in chaotic systems: a scaling law for the Shannon entropy and strong fluctuations of the 'effective Shannon entropy' along the transient, for k>kc.
120014368
A new proposal for the determination of the renormalization group trajectories by the Monte Carlo renormalization group method
Abstract We present a new method for calculating block renormalized couplings by Monte Carlo renormalization group. This method has several advantages with respect to the existing ones and can be applied for any value of the coupling constants. A preliminary numerical study of the 2-dimensional O(3) non linear σ-model is also presented.
121714112
A Monte Carlo simulation with an “improved” action for the O(3) non-linear sigma model
Abstract We present the results of a Monte Carlo simulation for a lattice action improved a la Symanzik. The results seem to give a faster approach of the lattice physics to its continuum limit.
121490138
On the effects of an uncertainty on the evolution law in dynamical systems
We show that a small perturbation of the evolution law of chaotic dynamical systems is practically equivalent to the finite precision on the knowledge of the initial condition. In spite of the short predictability time tp on a single trajectory we found that the statistical properties are not sensitive to small changes in the evolution law or initial probability distribution. This feature holds also for correlation functions at a delay larger than tp. We discuss the roundoff effects on integrable systems.
122714395
Passive-Scalar Fluctuations in Intermittent Turbulence
We discuss how the spatial intermittency of energy dissipation in 3D fully developed turbulence affects the small-scale statistics of passive scalars. We relate the passive-scalar behaviour to the diffusion properties of particle pairs in turbulent fluids. We thus find the intermittency correction to the -5/3 Obukhov-Corrsin law for the power spectrum of a passive scalar at wavenumber k where molecular diffusion and viscosity play a negligible role (inertial convective subrange). This correction is positive at difference with the negative correction to the -5/3 Kolmogorov law for the energy spectrum. We finally show that the structure functions of passive scalars have scaling exponents linear in the moment order, even in the framework of multifractal models.