Finite-Size Scaling in the Driven Lattice Gas

TL;DR

This study uses Monte Carlo simulations to analyze the finite-size scaling behavior of the driven lattice gas at high temperature, confirming theoretical predictions and revealing Gaussian transverse excitations.

Contribution

It introduces a finite-volume correlation length for the driven lattice gas and verifies its scaling properties, supporting the field theory predictions.

Findings

Correlation length has a well-defined infinite-volume limit.

Theoretical predictions for susceptibility and magnetization are confirmed.

Transverse Binder parameter vanishes at the critical point in all dimensions d≥2.

Abstract

We present a Monte Carlo study of the high-temperature phase of the two-dimensional 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 $d\ge 2$ 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.