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 r=-Tt. Here 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)=E0+C1rx, where x0.25, while for the 3D J, a two-layer J, and infinite-range models, E(r)=E0-C2(inr)-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. © 1986 The American Physical Society.