Comment on "Evidence for nontrivial ground-state structure of 3d +/- J spin glasses"

Abstract

In a recent Letter [Europhys. Lett. 40, 429 (1997)], Hartmann presented results for the structure of the degenerate ground states of the three-dimensional +/- J spin glass model obtained using a genetic algorithm. In this Comment, I argue that the method does not produce the correct thermodynamic distribution of ground states and therefore gives erroneous results for the overlap distribution. I present results of simulated annealing calculations using different annealing rates for cubic lattices with N=4*4*4spins. The disorder-averaged overlap distribution exhibits a significant dependence on the annealing rate, even when the energy has converged. For fast annealing, moments of the distribution are similar to those presented by Hartmann. However, as the annealing rate is lowered, they approach the results previously obtained using a multi-canonical Monte Carlo method. This shows explicitly that care must be taken not only to reach states with the lowest energy but also to ensure that they obey the correct thermodynamic distribution, i.e., that the probability is the same for reaching any of the ground states.