Replica bounds for diluted non-Poissonian spin systems

TL;DR

This paper extends replica bounds and free energy bounds to diluted spin-glass models with arbitrary degree distributions, introducing an interpolation method that connects to the cavity method and generalizes Ghirlanda-Guerra identities.

Contribution

It develops a new interpolation procedure for non-Poissonian graphs, broadening the applicability of replica bounds in spin-glass models.

Findings

Extended replica bounds to non-Poissonian graphs

Introduced an interpolation method linking to the cavity approach

Derived generalized Ghirlanda-Guerra identities

Abstract

In this paper we extend replica bounds and free energy subadditivity arguments to diluted spin-glass models on graphs with arbitrary, non-Poissonian degree distribution. The new difficulties specific of this case are overcome introducing an interpolation procedure that stresses the relation between interpolation methods and the cavity method. As a byproduct we obtain self-averaging identities that generalize the Ghirlanda-Guerra ones to the multi-overlap case.