Thermodynamic Identities and Symmetry Breaking in Short-Range Spin Glasses

TL;DR

This paper introduces a method to derive thermodynamic identities in short-range spin glasses, revealing how symmetry breaking and pure state structures relate to the underlying Hamiltonian and coupling distributions.

Contribution

It provides a novel technique to connect pure state weights, overlaps, and correlations directly from the Hamiltonian, applicable to general coupling distributions and different thermodynamic phases.

Findings

Relations hold in simple thermodynamic phases like droplet-scaling and chaotic pairs.

In nontrivial mixed-state phases, relations imply replica symmetry breaking via Derrida-Ruelle cascades.

Pure state weights follow a Poisson-Dirichlet distribution in symmetry-broken phases.

Abstract

We present a technique to generate relations connecting pure state weights, overlaps, and correlation functions in short-range spin glasses. These are obtained directly from the unperturbed Hamiltonian and hold for general coupling distributions. All are satisfied in phases with simple thermodynamic structure, such as the droplet-scaling and chaotic pairs pictures. If instead nontrivial mixed-state pictures hold, the relations suggest that replica symmetry is broken as described by a Derrida-Ruelle cascade, with pure state weights distributed as a Poisson-Dirichlet process.