The Cavity Approach for Metastable Glassy States Near Random First Order Phase Transitions

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It is shown that the cavity method developed to describe equilibrium states in the mean-field Ising spin glass model can be generalized to describe metastable states in the mean-field Potts glass. The crucial input is the existence of an extensive number of statistically similar but incongruent metastable states with a weighted Gaussian free energy distribution. It is argued that the inherent quenched randomness in the Potts glass Hamiltonian is not important for most of the arguments and that this approach provides insight into recent work on the structural glass problem.