Nonequilibrium evolution of window overlaps in spin glasses

We investigate numerically the time dependence of window overlaps in a three-dimensional Ising spin glass below its transition temperature after a rapid quench. Using an efficient GPU implementation, we are able to study large systems up to lateral length L = 128 and up to long times of t = 10(8) sweeps. We find that the data scales according to the ratio of the window size W to the nonequilibrium coherence length xi(t). We also show a substantial change in behavior if the system is run for long enough that it globally equilibrates, i.e., xi(t) approximate to L/2, where L is the lattice size. This indicates that the local behavior of a spin glass depends on the spin configurations (and presumably also the bonds) far away. We compare with similar simulations for the Ising ferromagnet. Based on these results, we speculate on a connection between the nonequilibrium dynamics discussed here and averages computed theoretically using the metastate.