The fluctuation-dissipation theorem and the linear Glauber model

TL;DR

This paper derives exact autocorrelation and response functions for the linear Glauber model, revealing that the fluctuation-dissipation ratio remains valid in stationary states despite lack of detailed balance in higher dimensions, and exhibits aging at criticality.

Contribution

It provides exact analytical expressions for correlation and response functions in a non-equilibrium linear spin model, highlighting fluctuation-dissipation behavior without detailed balance.

Findings

Fluctuation-dissipation ratio holds in stationary regime.

Aging occurs in the transient regime.

At criticality, the fluctuation-dissipation ratio approaches 1/2.

Abstract

We obtain exact expressions for the two-time autocorrelation and response functions of the $d$-dimensional linear Glauber model. Although this linear model does not obey detailed balance in dimensions $d\geq 2$, we show that the usual form of the fluctuation-dissipation ratio still holds in the stationary regime. In the transient regime, we show the occurence of aging, with a special limit of the fluctuation-dissipation ratio, $X_{\infty}=1/2$, for a quench at the critical point.