Metastable states in spin glasses with short-ranged interactions

Abstract

A formalism is developed for calculating the density N_S(E) of metastable (i.e. one spin-flip stable) states of energy E for Ising spin glasses. Results are presented, for nearest-neighbour interactions on hypercubic lattices to O(1/z), where z is the coordination number, for E>or=E_c, a critical energy below which the metastable states become correlated. The critical behaviour associated with the transition at E_c is non-classical in less than six dimensions, with critical exponents identical to those of the thermal spin glass transition. Results are also presented for an asymmetric distribution of exchange interactions.