Critical behavior of nonequilibrium q-state systems

TL;DR

This paper investigates two classes of nonequilibrium q-state models on lattices, analyzing their critical behavior, phase transitions, and critical exponents, with special cases reducing to well-known models like Ising and percolation.

Contribution

It introduces and analyzes two novel nonequilibrium models with q-valued spins, extending understanding of critical phenomena beyond equilibrium systems.

Findings

Critical points and exponents estimated in 2D.

Models reduce to Ising for q=2 and to percolation for q=∞.

Breaking detailed balance except at specific q values.

Abstract

We present two classes of nonequilibrium models with critical behavior. Each model is characterized by an integer $q>1$, and is defined on configurations of $q$-valued spins on regular lattices. The definitions of the models are very similar to the updating rules in Wolff's algorithm for the Potts model, but both classes break detailed balance, except for $q=2$ and $q=\infty$. In the first case both models reduce to the Ising model, while one of them reduces to percolation (more precisely, to the general epidemic process) for $q=\infty$. Locations of the critical point and critical exponents are estimated in 2 dimensions.