Continuum Field Description of Driven Lattice Gases

TL;DR

This paper reviews the critical behavior of the Driven Lattice Gas, introduces a new Langevin equation depending on microscopic transition probabilities, and classifies different driving field regimes into universality classes.

Contribution

It presents a novel Langevin equation for the DLG that incorporates microscopic transition probabilities and analyzes the impact of driving field strength on universality classes.

Findings

Finite and infinite driving fields belong to different universality classes.

The RDLG with infinite average field shares universality with the infinitely driven DLG.

A Langevin equation for the two-layer DLG is also derived.

Abstract

We review the critical behaviour of the Driven Lattice Gas (DLG) model. As a result, we obtain a novel Langevin equation for the DLG which depends on the microscopic transition probabilities. We then show how this dependence affects the critical behaviour of the the DLG placing the finite and the infinite driving field cases into different universality classes. Two other well known anisotropic, conservative, non-equilibrium models, the two-temperature model and the randomly driven model (RDLG) are also studied. It is shown that the RDLG with infinite averaged field and the two-temperature model with infinite parallel temperature fall in the same universality class as the infinitely driven DLG. A Langevin equation for the two-layer DLG is also presented.