123292838
The non-linear sigma model: 3-loop renormalization and lattice scaling
Abstract We present a perturbative calculation of the first non-universal terms of the renormalization group functions for the non-linear σ-model regularized on a lattice, for a choice of different lattice actions. Such terms, hitherto unknown, fix the leading corrections to universal asymptotic scaling. However, by comparing with Monte Carlo simulations, one sees that the actual deviations from universal scaling are due to non-perturbative effects, and not to perturbative analytic corrections. The latter are nonetheless relevant to determine the ratios of scaling operators to Λ-parameters.
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.
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.
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.
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.
12041139
The flat phase of fixed-connectivity membranes
Abstract The statistical mechanics of flexible two-dimensional surfaces (membranes) appears in a wide variety of physical settings. In this talk we discuss the simplest case of fixed-connectivity surfaces. We first review the current theoretical understanding of the remarkable flat phase of such membranes. We then summarize the results of a recent large scale Monte Carlo simulation of the simplest conceivable discrete realization of this system [1]. We verify the existence of long-range order, determine the associated critical exponents of the flat phase and compare the results to the predictions of various theoretical models.
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.
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.
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.
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.