Stability of the Spin Glass Phase under Perturbations

TL;DR

This paper develops a new linear response stability theory for spin glasses, showing that certain perturbations preserve the structural identities defining the spin glass phase.

Contribution

It introduces a novel stability framework that links perturbations to the structural identities of the spin glass phase.

Findings

Established a linear response stability theory for spin glasses.

Proved stability under perturbations implies structural identities.

Enhanced understanding of the robustness of the spin glass phase.

Abstract

We introduce and prove a novel linear response stability theory for spin glasses. The new stability under suitable perturbation of the equilibrium state implies the whole set of structural identities that characterize the spin glass phase.