An exact relation between free energy fluctuations and bond chaos in the Sherrington-Kirkpatrick model

TL;DR

This paper establishes an exact mathematical relation between free energy fluctuations and bond chaos in the Sherrington-Kirkpatrick spin glass model, providing new insights into the model's behavior.

Contribution

It introduces a novel exact relation linking free energy fluctuations and bond chaos using an interpolating Hamiltonian technique.

Findings

Derived an upper bound for free energy fluctuations.

Established a precise connection between bond chaos and free energy variability.

Provided a new analytical tool for studying spin glass models.

Abstract

Using a variant of the interpolating Hamiltonian technique, we show that there exists, in the Sherrington-Kirkpatrick spin glass, an exact connection between the sample-to-sample fluctuations of the free energy and bond chaos involving 2- and 4-replica overlaps between replicas with different but correlated bonds. This relation is used to derive an upper bound of the fluctuations.