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

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

The fluctuation-dissipation theorem and the linear Glauber model

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.Comment: Accepted for publication (Physical Review E