Stochastic Stability and the Spin Glass Phase. The State of the Art for Mean Field and Finite Dimensional Models

TL;DR

This paper explores invariance properties in spin glass phases, demonstrating their implications for overlap distributions and comparing mean field and finite dimensional models to understand their stability and behavior.

Contribution

It introduces invariance principles under perturbations in spin glasses and discusses their consequences, providing a comparative analysis of mean field and finite dimensional models.

Findings

Invariance properties lead to factorization rules for overlaps.

Comparison highlights differences and similarities between model types.

Implications for understanding spin glass stability and phase structure.

Abstract

Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean field and finite dimensional models is shortly discussed.