123419934
Complex singularities in the specific heat of the SU(2) lattice gauge model
Abstract A recent Monte Carlo simulation showing a sharp peak versus β in the specific heat for an SU(2) lattice gauge theory is compared with the high temperature expansion. An interpretation based on complex β -plane singularities is proposed.
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.
123085141
Intermittency and Multifractality in Magnetic Dynamos
We study the convection of magnetic fields in the presence of Lagrangian chaos, i.e. when nearby fluid elements diverge exponentially in time. We show that the magnetic field is of a multifractal nature as a consequence of the spatial fluctuations in the exponential growth of the field. We provide numerical and theoretical evidence that the magnetic fields can concentrate in small domains of a fluid with weak Lagrangian chaos. Moreover, these properties are relevant also for the study of the case of small but nonzero magnetic diffusivity.
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.
121504553
On the masses of the glueballs in pure SU(2) lattice gauge theory
Abstract Using a Monte Carlo method to measure the correlation functions of different quantities, the mass spectrum of the glue-ball is investigated for an SU(2) gauge model in an 8 4 lattice.
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.
16467100
The Flat Phase of Crystalline Membranes
We present the results of a high-statistics Monte Carlo simulation of a phantorn crystalline (fixed-connectivity) membrane with free boundary. We verify trie existence of a fiai phase by exarnining lattices of size up to 128~. The Harniltonian of the rnodel is trie sum of a simple spnng pair potential, with no hard-core repulsion, and beuding energy. The only free pararneter is the bending ngidity ~. In-plane elastic constants are non explicitly introduced. We obtain the rernarkable result thon this simple model dynamically generates the elastic constants required to stabilize the fiai phase. We present measurements of the size (Flory) exportent v and the roughness exportent (. We also determine the critical exponents ~ and ~u descnbing the scale dependence of the bending rigidity (~(q) mJ q~~) and trie mduced elastic constants (A(q)mJ ~1(q) ~J q~~ ). Ai bending rigidity ~ = l-1, we find v = 0.95(5) (Hausdorlf dimension dH = 2 Iv = 2,1(1)), ( = 0.64(2 and ~u = 0.50(1). These results are consistent with the scaling relation ( = (2 + ~u)/4. The additional scaling relation ~ = 2(1- () irnplies ~ = 0.72(4). A direct measurernent of ~ from the power-law decay of the normal-normal correlation functiou yields ~ m 0.6 on the 128~ lattice.
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.
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.
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.
8220387
Phantom Tubules
We provide the first numerical evidence for the existence of the tubule phase, predicted by Radzihovsky and Toner (RT), for anisotropic tethered membranes. Incorporating anisotropy into the bending rigidity of a simple model of a phantom tethered membrane with the topology of a disk and free boundary conditions we show that the model indeed has two phase transitions corresponding to the flat-to-tubule and tubule-to-crumpled transitions. For the tubule phase we measure the Flory exponent νF , describing the growth of the tubule radius with the extent of the tubule, and the roughness exponent ζ, which measures the r.m.s. height fluctuations in the extended direction. We find νF = 0.305(14) and ζ = 0.895(60) which are in reasonable agreement with the theoretical predictions of RT, νF = 1/4 and ζ = 1. PACS numbers: 64.60.Fr, 05.40.+j, 82.65.Dp Typeset using REVTEX