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

Abstract

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)\ensuremath{\cdot}${\mathrm{S}}_{i}$(t)〉\ensuremath{\sim}${t}_{\mathit{c}}^{\ensuremath{-}\ensuremath{\lambda}}$/z, where z is the usual dynamic critical exponent. Naively, ${\ensuremath{\lambda}}_{c}$=d, but I find ${\ensuremath{\lambda}}_{c}$simulations of pure Ising models in d=2, 3 and the \ifmmode\pm\else\textpm\fi{}J Ising spin glass in d=3. This suggests that ${\ensuremath{\lambda}}_{c}$ 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 ${\ensuremath{\lambda}}_{c}$/z observed in the spin-glass simulation is in good agreement with a recent experimental measurement by Granberg et al.