METASTABLE STATES OF AN ASYMMETRIC SPIN-GLASS WITH ONE STORED PATTERN

The number of metastable states in a spin-glass with asymmetric Gaussi an couplings (J(ij) not-equal J(ji)) is studied. In order to store one pattern a generalized stability condition on the local energies is co nsidered for a part of the system (alpha = n/N) only. The average numb er of metastable states is calculated analytically as a function of th e overlap m in the thermodynamic limit. For the contribution of the st orage restriction an approximation is introduced to simplify the calcu lations. The corresponding saddle-point equations are solved numerical ly for two distribution functions of the local energies. For several v alues of the parameters we find two bands with an exponential number o f metastable states. At a critical value alpha(crit) the second band d isappears. The critical value for the storage parameter is calculated numerically. As expected we find alpha(crit) --> 1 for sigma --> 0.