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We investigate numerically the time dependence of "window" overlaps in athree-dimensional Ising spin glass below its transition temperature after arapid quench. Using an efficient GPU implementation, we are able to study largesystems 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 $W$ tothe non-equilibrium coherence length $\xi(t)$. We also show a substantialchange in behavior if the system is run for long enough that it globallyequilibrates, i.e. $\xi(t) \approx L/2$, where $L$ is the lattice size. Thisindicates that the local behavior of a spin glass depends on the spinconfigurations (and presumably also the bonds) far away. We compare withsimilar simulations for the Ising ferromagnet. Based on these results, wespeculate on a connection between the non-equilibrium dynamics discussed hereand averages computed theoretically using the "metastate".

Non-equilibrium evolution of window overlaps in spin glasses