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.