Metastable states of the naive mean-field model for spin glasses at finite temperatures

Abstract

The authors investigate statistical-mechanical organization of metastable states at finite temperatures in the naive mean-field model for spin glasses by direct numerical analysis on the equations of states of the model. The number of their solutions (metastable states) is shown to agree with the replica prediction developed by Bray and Moore (1980). Furthermore, such sophisticated spin-glass properties as the universal probability law of the nonself-averaging overlap probability of metastable states, which are initially derived for the Sherrington-Kirkpatrick model by means of the replica argument, are demonstrated to be common also to the naive mean-field model.