Anisotropic finite-size scaling analysis of a three-dimensional driven-diffusive system

TL;DR

This study investigates the critical behavior of a three-dimensional driven diffusive system using extensive finite-size scaling analysis, testing various theoretical predictions against numerical data to identify the most accurate description.

Contribution

It provides a comprehensive numerical analysis that evaluates and compares multiple existing theories for the critical behavior of 3D driven diffusive systems.

Findings

Leung's version including dangerous irrelevant variables fits data better.

Binder and Wang's prediction does not match the data well.

Isotropic finite-size scaling is inconsistent with cubic system data.

Abstract

We study the standard three-dimensional driven diffusive system on a simple cubic lattice where particle jumps along a given lattice direction are biased by an infinitely strong field, while those along other directions follow the usual Kawasaki dynamics. Our goal is to determine which of the several existing theories for critical behavior is valid. We analyze finite-size scaling properties using a range of system shapes and sizes far exceeding previous studies. Four different analytic predictions are tested against the numerical data. Binder and Wang's prediction does not fit the data well. Among the two slightly different versions of Leung, the one including the effects of a dangerous irrelevant variable appears to be better. Recently proposed isotropic finite-size scaling is inconsistent with our data from cubic systems, where systematic deviations are found, especially in scaling at the critical temperature.