Phase diagram of the naive mean-field model for spin glasses

Abstract

The replica-symmetry-breaking solution is formulated for the infinite-ranged binomial spin glass model, which is a generalization of the Sherrington-Kirkpatrick (SK) model and includes the Bray-Sompolinsky-Yu (BSY) model as a limit. In the formulation it is found that the Parisi equation is the same as the original one for the SK model. This fact is used to show that the boundary between the spin glass phase and the mixed phase is independent of temperature, which is confirmed by numerical analysis of the naive mean-field equations and completes the phase diagram of the BSY model.