Aging and fluctuation-dissipation ratio in a nonequilibrium $q$-state lattice model

TL;DR

This paper introduces a symmetric nonequilibrium $q$-state lattice model, derives exact two-time functions, and analyzes aging and fluctuation-dissipation behavior, confirming theoretical predictions in a generalized setting.

Contribution

It extends the linear Glauber model to $q$ states, providing exact autocorrelation and response functions, and explores aging and fluctuation-dissipation ratios in this generalized framework.

Findings

Fluctuation-dissipation theorem holds in the stationary regime.

Aging behavior observed in the transient regime.

Fluctuation-dissipation ratio matches linear Glauber model predictions.

Abstract

A generalized version of the nonequilibrium linear Glauber model with $q$ states in $d$ dimensions is introduced and analyzed. The model is fully symmetric, its dynamics being invariant under all permutations of the $q$ states. Exact expressions for the two-time autocorrelation and response functions on a $d$-dimensional lattice are obtained. In the stationary regime, the fluctuation-dissipation theorem holds, while in the transient the aging is observed with the fluctuation-dissipation ratio leading to the value predicted for the linear Glauber model.