Self-Averaging Identities for Random Spin Systems

TL;DR

This paper develops a general framework for self-averaging identities in spin systems, proving their validity across diverse models including dilute spin glasses, and extends known identities like Ghirlanda-Guerra and Aizenman-Contucci.

Contribution

It introduces a model-agnostic method to establish self-averaging identities, broadening their applicability in spin system analysis.

Findings

Proves Ghirlanda-Guerra and Aizenman-Contucci identities in a wide class of models.

Provides a systematic approach applicable to various spin systems.

Extends identities to dilute spin glasses.

Abstract

We provide a systematic treatment of self-averaging identities for various spin systems. The method is quite general, basically not relying on the nature of the model, and as a special case recovers the Ghirlanda-Guerra and Aizenman-Contucci identities, which are therefore proven, together with their extension, to be valid in a vaste class of spin models. We use the dilute spin glass as a guiding example.