Ghirlanda-Guerra identities and cavity equations for diluted spin glass models

Abstract

This note supplies the details of the cavity lower bound used in "The Mézard-Parisi formula" [8]. Specifically, we show that small perturbations that do not change the limiting free energy can be chosen so that the asymptotic Gibbs measures arising in the Aizenman-Sims-Starr lower bound satisfy both the Ghirlanda-Guerra identities and the cavity equations. These calculations are standard and require only minor modifications of arguments already available in the literature. We record them here for completeness, avoiding a lengthy repetition of these arguments in [8].