Recipes for Metastable States in Spin Glasses

In this paper we develop further a method recently introduced by one of us to study metastable states in spin glasses. We consider a `potentional function', defined as the free energy of a system at a given temperature T constrained to have a fixed overlap with a reference configuartion of equilibrium at temperature T'. We apply the method to the spherical p-spin glass, and to some generalization, of this model in the range of temperatures between the dynamic and the static transition. The analysis suggests a correspondence among local minima of the potential and metastable states. This correspondence is confirmed studying the relaxation dynamics at temperature T of a system starting from an initial configuration equilibrated at a different.