LANDSCAPE STATISTICS OF THE P-SPIN ISING-MODEL

The statistical properties of the local optima (metastable states) of the infinite-range Ising spin glass with p-spin interactions in the pr esence of an external magnetic field h are investigated analytically. The average number of optima as well as the typical overlap between pa irs of identical optima are calculated for general p. Similarly to the thermodynamic order parameter, for p > 2 and small h, the typical ove rlap q(t) is a discontinuous function of the energy. The size of the j ump in q(t) increases with p and decreases with h, vanishing at finite values of the magnetic field.