The Ghirlanda-Guerra Identities

TL;DR

This paper discusses the conditions under which Gaussian spin-glass models satisfy the Ghirlanda-Guerra identities, focusing on the growth of the Hamiltonian's variance relative to the volume.

Contribution

It establishes that Gaussian spin-glass models with Hamiltonian variance growing proportionally to volume fulfill the Ghirlanda-Guerra identities.

Findings

Ghirlanda-Guerra identities hold when variance grows with volume

Normalized Hamiltonian covariance is key to identities

Provides conditions for identities in Gaussian spin glasses

Abstract

If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.