Fluctuation dissipation ratio in the one dimensional kinetic Ising model

Abstract

The exact relation between the response function $R(t,t^{\prime })$ and the two time correlation function $C(t,t^{\prime })$ is derived analytically in the one dimensional kinetic Ising model subjected to a temperature quench. The fluctuation dissipation ratio $X(t,t^{\prime })$ is found to depend on time through $C(t,t^{\prime })$ in the time region where scaling $C(t,t^{\prime })=f(t/t^{\prime })$ holds. The crossover from the nontrivial form $X(C(t,t^{\prime }))$ to $X(t,t^{\prime })\equiv 1$ takes place as the waiting time $t_w$ is increased from below to above the equilibration time $t_{eq}$.

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• Effective temperatures out of equilibrium

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