Remanent magnetization decay at the spin-glass critical point: A new dynamic critical exponent for nonequilibrium autocorrelations

A quench of a d-dimensional spin system from a random initial configuration, {${\mathrm{S}}_i$(0)}, to a critical point is considered. The decay with time t of the autocorrelation with the initial condition is $q_0$(t)==〈${\mathrm{S}}_i$(0)⋅${\mathrm{S}}_i$(t)〉∼$t_{\mathit{c}}^{-\lambda }$/z, where z is the usual dynamic critical exponent. Naively, ${\lambda }_c$=d, but I find ${\lambda }_c$ d=2, 3 and the ±J Ising spin glass in d=3. This suggests that ${\lambda }_c$ is a new critical exponent for nonequilibrium dynamics. For a spin glass the decay of $q_0$(t) is the same as that of the remanent magnetization; the exponent ${\lambda }_c$/z observed in the spin-glass simulation is in good agreement with a recent experimental measurement by Granberg et al.