The overlap in glassy systems

TL;DR

This paper reviews various definitions and recent findings on the overlap and its distribution in glassy systems, highlighting their relation to fluctuation dissipation relations in spin glasses.

Contribution

It synthesizes different approaches to overlap definitions and presents recent results on local overlap distributions in spin glasses.

Findings

Recent results on local overlap distributions in spin glasses

Connections between overlap and fluctuation dissipation relations

Comparison of various overlap definitions

Abstract

In this paper I will consider many of the various definitions of the overlap and of its probability distribution that have been introduced in the literature starting from the original papers of Edwards and Anderson; I will present also some of the most recent results on the probability distribution of the local overlap in spin glasses. These quantities are related to the fluctuation dissipation relations both in their local and in their global versions.