Local overlaps, heterogeneities and the local fluctuation dissipation relations

TL;DR

This paper introduces the probability distribution of local overlaps in spin glasses and demonstrates their role in local fluctuation dissipation relations, providing insights into aging phenomena and effective temperatures.

Contribution

It develops a theoretical framework linking local overlaps to fluctuation dissipation relations using stochastic stability principles.

Findings

Local overlaps have a well-defined probability distribution.

Local fluctuation dissipation relations can be proved using local overlaps.

All sites in an aging experiment share the same effective temperature.

Abstract

In this paper I introduce the probability distribution of the local overlap in spin glasses. The properties of the local overlaps are studied in details. These quantities are related to the recently proposed local version of the fluctuation dissipation relations: using the general principle of stochastic stability these local fluctuation dissipation relations can be proved in a way that is very similar to the usual proof of the fluctuation dissipation relations for intensive quantities. The local overlap and its probability distribution play a crucial role in this proof. Similar arguments can be used to prove that all sites in an aging experiment stay at the same effective temperature at the same time.