Cooling-rate dependence for the spin-glass ground-state energy: Implications for optimization by simulated annealing.

The zero-temperature ground-state properties of five spin-glass models have been studied as a function of the cooling rate requivalent-..delta..T/t. Here ..delta..T is the temperature decrement and t is the time (in Monte Carlo steps) at each temperature T. For the 2D +- J and Gaussian models, E(r) = E/sub 0/+C/sub 1/r/sup x/, where xapeq 20.25 while for the 3D +- J, a two-layer +- J and infinite-range models, E(r) = E/sub 0/-C/sub 2/(lnr)/sup -1/. We speculate that this difference is related to the fact that the 2D models are not NP-complete while the other three models are.