Replica equivalence in the Edwards-Anderson model

TL;DR

This paper demonstrates that the Edwards-Anderson spin-glass model exhibits replica equivalence, a property related to the structure of equilibrium states, extending concepts from mean-field theory to finite-dimensional models.

Contribution

It establishes the presence of replica equivalence in finite-dimensional spin-glass models using stochastic stability, generalizing mean-field ultrametricity concepts.

Findings

Replica equivalence holds in the Edwards-Anderson model.

The proof relies on stochastic stability and fluctuation control.

Results apply to all finite-dimensional spin-glass models.

Abstract

After introducing and discussing the "link-overlap" between spin configurations we show that the Edwards-Anderson model has a "replica-equivalent" quenched equilibrium state, a property introduced by Parisi in the description of the mean-field spin-glass phase which generalizes ultrametricity. Our argument is based on the control of fluctuations through the property of stochastic stability and works for all the finite-dimensional spin-glass models.