Replica and Glasses

TL;DR

This paper reviews the theoretical framework of spin glasses, focusing on the replica method, stochastic stability, and their implications for system dynamics, supported by simulations and awaiting experimental validation.

Contribution

It highlights the broader applicability of the replica method beyond quenched disorder and discusses recent insights into stochastic stability in spin glasses.

Findings

Replica method's probabilistic implications emphasized

Stochastic stability's importance in spin glasses highlighted

Simulation results support theoretical predictions

Abstract

In these two lectures I 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