Finite-Size Scaling in the Driven Lattice Gas

Abstract

We present a Monte Carlo study of the high-temperature phase of the twodimensional driven lattice gas at infinite driving field. We define a finite-volume correlation length, verify that this definition has a good infinite-volume limit independent of the lattice geometry, and study its finite-size-scaling behavior. The results for the correlation length are in good agreement with the predictions based on the field theory proposed by Janssen, Schmittmann, Leung, and Cardy. The theoretical predictions for the susceptibility and the magnetization are also well verified. We show that the transverse Binder parameter vanishes at the critical point in all dimensions d ≥ 2 and discuss how such result should be expected in the theory of Janssen et al. in spite of the existence of a dangerously irrelevant operator. Our results confirm the Gaussian nature of the transverse excitations.

Twenty Five Years After KLS: A Celebration of Non-equilibrium Statistical Mechanics

“…Thus, we expect these predictions to be reliable down to d = 2, without the necessity of Borel resummation [34]. These novel critical properties are largely confirmed in extensive simulation studies [37][38][39]. Despite lingering controversies associated with claims to the contrary [40], no other field theoretic description is free of deficiencies at the basic level of symmetries [41].…”

Universal Gaussian behavior of driven lattice gases at short times

“…Beyond its widespread applications in equilibrium statistical physics, it has also been used in the context of nonequilibrium lattice gases in order to characterize the stationary-state behavior [25,30]. More recently, g has been used to show that the dynamical behavior of the first nontrivial transverse mode is well described by a Gaussian theory up to a time which scales as L z ⊥ in all the three different lattice gas models [20].…”

“…upon increasing the system size L ⊥ [30]. To connect the prediction of the scaling theory with that of the Gaussian theory, we need to express the behavior of m S as a function of the isotropic aspect ratio L ⊥ /L .…”

“…Its appropriate definition for systems with conserved order parameter has been proposed in Ref. [30],…”

Nonequilibrium Relaxation and Critical Aging for Driven Ising Lattice Gases

“…In the absence of the drive, one recovers the equilibrium Ising model ferromagnetic phase transition. Yet the correct longwavelength description of the KLS Ising driven lattice gas at the critical point has been subject to a lasting debate [8][9][10][11][12][13]. Ambiguities in determining the critical exponents are in part caused by exceedingly slow crossovers to the asymptotic regime [13]; also, it is crucial to implement the proper anisotropic lattice scaling, and infer scaling exponents sufficiently close to the critical point [14].…”