On the replica method for glassy systems

TL;DR

This paper reviews the replica method in spin glasses, emphasizing its probabilistic implications and applicability beyond quenched disorder, with insights into system dynamics supported by simulations.

Contribution

It highlights the importance of stochastic stability in the replica method and extends its relevance to systems without quenched disorder.

Findings

Replica method's probabilistic consequences are significant.

Large-scale simulations confirm theoretical predictions.

Experimental verification remains pending.

Abstract

In this talk we review our theoretical understanding of spin glasses paying a particular attention to the basic physical ideas. We introduce the replica method and we describe its probabilistic consequences (we stress the recently discovered importance of stochastic stability). We show that the replica method is not restricted to systems with quenched disorder. We present the consequences on the dynamics of the system when it slows approaches equilibrium are presented: they are confirmed by large scale simulations, while we are still awaiting for a direct experimental verification.