The fluctuation-dissipation relation in an Ising model without detailed balance

Abstract

We consider the modified Ising model introduced by de Oliveira et al. [J.Phys.A {\bf 26}, 2317 (1993)], where the temperature depends locally on the spin configuration and detailed balance and local equilibrium are not obeyed. We derive a relation between the linear response function and correlation functions which generalizes the fluctuation-dissipation theorem. In the stationary states of the model, which are the counterparts of the Ising equilibrium states, the fluctuation-dissipation theorem breaks down due to the lack of time reversal invariance. In the non-stationary phase ordering kinetics the parametric plot of the integrated response function $\chi (t,t_w)$ versus the autocorrelation function is different from that of the kinetic Ising model. However, splitting $\chi (t,t_w)$ into a stationary and an aging term $\chi (t,t_w)={\chi }_{st}(t-t_w)+{\chi }_{ag}(t,t_w)$, we find ${\chi }_{ag}(t,t_w)\sim t_w^{-a_{\chi }}f(t/t_w)$, and a numerical value of $a_{\chi }$ consistent with $a_{\chi }=1/4$, as in the kinetic Ising model.

17 pages, 15 figures. To appear on Physical Review E

References in corpus (2)

• Bona Fide Thermodynamic Temperature in Nonequilibrium Kinetic Ising Models
• Generic features of the fluctuation dissipation relation in coarsening systems

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• Relaxation processes in a system with logarithmic growth
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