Interaction Flip Identities for non Centered Spin Glasses

TL;DR

This paper studies how flipping interactions in subregions of non-centered spin glasses affects free energies, deriving polynomial identities through fluctuation bounds and martingale methods.

Contribution

It introduces a new approach using fluctuation bounds and martingale techniques to derive identities in non-centered spin glass models.

Findings

Derived polynomial identities involving overlaps and magnetizations.

Established fluctuation bounds for free energy changes.

Provided insights into the structure of non-centered spin glasses.

Abstract

We consider spin glass models with non-centered interactions and investigate the effect, on the random free energies, of flipping the interaction in a subregion of the entire volume. A fluctuation bound obtained by martingale methods produces, with the help of integration by parts technique, a family of polynomial identities involving overlaps and magnetizations.