Free energy of mean-field spin-glass models: Evolution operator and perturbation expansion


We introduce a perturbation expansion for the evolution operator used to represent free energy with continuous replica-symmetry breaking in mean-field spin-glas models. We obtain a generic scheme for an approximate calculation of physical quantities of different mean-field spin-glass models at all temperatures. The first correction with a continuous order-parameter function beyond the approximation with one level of replica-symmetry breaking is explicitly evaluated in the glassy phase of the Sherrington-Kirkpatrick model.