Cumulants of the three state Potts model and of nonequilibrium models with C3v symmetry

TL;DR

This study investigates the critical behavior of two-dimensional C3v symmetric lattice gas models, including the three-state Potts model and irreversible models, revealing universal cumulant values unaffected by irreversibility.

Contribution

It demonstrates that irreversibility does not alter the critical cumulant behavior in C3v symmetric models, establishing universality across equilibrium and nonequilibrium systems.

Findings

Universal Binder cumulant value U* for both models.

Irreversibility does not affect critical behavior.

Consistent third-order cumulant behavior observed.

Abstract

The critical behavior of two-dimensional stochastic lattice gas models with C3v symmetry is analyzed. We study the cumulants of the order parameter for the three state (equilibrium) Potts model and for two irreversible models whose dynamic rules are invariant under the symmetry operations of the point group C3v. By means of extensive numerical analysis of the phase transition we show that irreversibility does not affect the critical behavior of the systems. In particular we find that the Binder reduced fourth order cumulant takes a universal value U* which is the same for the three state Potts model and for the irreversible models. The same universal behavior is observed for the reduced third-order cumulant.