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-/z, where z is the usual dynamic critical exponent. Naively, c=d, but I find c<d in simulations of pure Ising models in d=2, 3 and the J Ising spin glass in d=3. This suggests that c 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 c/z observed in the spin-glass simulation is in good agreement with a recent experimental measurement by Granberg et al.