Equilibrium valleys in spin glasses at low temperature - art. no. 184413

We investigate the three-dimensional Edwards-Anderson spin glass model at l ow temperature on simple cubic lattices of sizes up to L = 12. Our findings show a strong continuity among T > 0 physical features and those found pre viously at T = 0, leading to a scenario with emerging mean field like chara cteristics that are enhanced in the large volume limit. For instance, the p icture of space filling sponges seems to survive in the large volume limit at T > 0. while entropic effects play a crucial role in determining the fre e-energy degeneracy of our finite volume states. All of our analysis is app lied to equilibrium configurations obtained by a parallel tempering on 512 different disorder realizations. First. we consider the spatial properties of the sites where pairs of independent spin configurations differ and we i ntroduce a modified spin overlap distribution which exhibits a nontrivial l imit for large L. Second, after removing the Z(2) (+/-1) symmetry, we clust er spin configurations into valleys. On average these valleys have free-ene rgy differences of O(1), but a difference in the (extensive) internal energ y that grows significantly with L; there is thus a large interplay between energy and entropy fluctuations. We also find that valleys typically differ by spongelike space filling clusters, just as found previously for low-ene rgy system-size excitations above the ground state.