Interaction-Flip Identities in Spin Glasses

TL;DR

This paper investigates how flipping interactions in spin glasses affects free and internal energy fluctuations, deriving new identities and bounds that enhance understanding of their equilibrium states.

Contribution

It introduces a novel interpolation method extending to the entire circle, leading to new overlap identities and insights into spin glass behavior.

Findings

Variance of energy difference grows with volume of flipped region

New overlap identities for equilibrium states are established

Non-interacting random field case analyzed and overlap triviality proved

Abstract

We study the properties of fluctuation for the free energies and internal energies of two spin glass systems that differ for having some set of interactions flipped. We show that their difference has a variance that grows like the volume of the flipped region. Using a new interpolation method, which extends to the entire circle the standard interpolation technique, we show by integration by parts that the bound imply new overlap identities for the equilibrium state. As a side result the case of the non-interacting random field is analyzed and the triviality of its overlap distribution proved.