Chaos in the mixed even-spin models

TL;DR

This paper rigorously investigates chaos phenomena in coupled mixed even-spin models, demonstrating how small parameter differences lead to concentrated overlaps, using advanced mathematical techniques.

Contribution

It introduces new identities and extends existing bounds to prove chaos in temperature, disorder, and external field for coupled spin glass models.

Findings

Proves chaos in temperature for coupled models.

Addresses chaos in disorder and external field.

Develops new mathematical identities and bounds.

Abstract

We consider a disordered system obtained by coupling two mixed even-spin models together. The chaos problem is concerned with the behavior of the coupled system when the external parameters in the two models, such as, temperature, disorder, or external field, are slightly different. It is conjectured that the overlap between two independently sampled spin configurations from, respectively, the Gibbs measures of the two models is essentially concentrated around a constant under the coupled Gibbs measure. Using the extended Guerra replica symmetry breaking bound together with a recent development of controlling the overlap using the Ghirlanda-Guerra identities as well as a new family of identities, we present rigorous results on chaos in temperature. In addition, chaos in disorder and in external field are addressed.