Metastable states of an asymmetric spin-glass with one stored pattern

Abstract

The number of metastable states in a spin-glass with asymmetric Gaussian couplings (J ij ≠J ji ) is studied. In order to store one pattern a generalized stability condition on the local energies is considered for a part of the system (α=n/N) only. The average number of metastable states is calculated analytically as a function of the overlapm in the thermodynamic limit. For the contribution of the storage restriction an approximation is introduced to simplify the calculations. The corresponding saddlepoint equations are solved numerically for two distribution functions of the local energies. For several values of the parameters we find two bands with an exponential number of metastable states. At a critical value αcrit the second band disappears. The critical value for the storage parameter is calculated numerically. As expected we find αcrit→1 for δ→0.