A Study of Two-Temperature Non-Equilibrium Ising Models: Critical Behavior and Universality

TL;DR

This paper investigates non-equilibrium 2D Ising models with competing heat-bath temperatures, comparing different dynamics to understand their critical behavior and universality classes, revealing some share the same critical exponents as equilibrium models.

Contribution

It provides a comparative analysis of non-equilibrium Ising models with various dynamics and demonstrates their universality class similarities to equilibrium models.

Findings

Some non-equilibrium dynamics share the same critical exponents as equilibrium 2D Ising.

The bond Swendsen-Wang algorithm maps to an equilibrium model at an effective temperature.

Critical behavior is consistent across different non-equilibrium dynamics.

Abstract

We study a class of 2D non-equilibrium Ising models based on competing dynamics induced by contact with heat-baths at two different temperatures. We make a comparative study of the non-equilibrium versions of Metropolis, heat bath/Glauber and Swendsen-Wang dynamics and focus on their critical behavior in order to understand their universality classes. We present strong evidence that some of these dynamics have the same critical exponents and belong to the same universality class as the equilibrium 2D Ising model. We show that the bond version of the Swendsen-Wang update algorithm can be mapped into an equilibrium model at an effective temperature.