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, {Sᵢ(0)}, to a critical point is considered. The decay with time t of the autocorrelation with the initial condition is q₀(t)==〈Sᵢ(0){·}Sᵢ(t)〉{~}tc^-λ/z, where z is the usual dynamic critical exponent. Naively, λc=d, but I find λcsimulations of pure Ising models in d=2, 3 and the ±{}J Ising spin glass in d=3. This suggests that λc is a new critical exponent for nonequilibrium dynamics. For a spin glass the decay of q₀(t) is the same as that of the remanent magnetization; the exponent λc/z observed in the spin-glass simulation is in good agreement with a recent experimental measurement by Granberg et al.