Geometry and temperature chaos in mixed spherical spin glasses at low temperature - the perturbative regime

TL;DR

This paper investigates the low-temperature behavior of mixed spherical p-spin glass models, revealing how the Gibbs measure concentrates around critical points and explaining the occurrence of temperature chaos in these models.

Contribution

It demonstrates the concentration of the Gibbs measure on spherical bands around critical points and explains temperature chaos in mixed models near the 1-RSB regime.

Findings

Gibbs measure concentrates on spherical bands around critical points.

Critical points are pairwise orthogonal at different low temperatures.

Temperature chaos occurs in mixed models but not in pure spherical models.

Abstract

We study the Gibbs measure of mixed spherical $p$-spin glass models at low temperature, in (part of) the 1-RSB regime, including, in particular, models close to pure in an appropriate sense. We show that the Gibbs measure concentrates on spherical bands around deep critical points of the (extended) Hamiltonian restricted to the sphere of radius $\sqrt N q_\star$, where $q_\star^2$ is the rightmost point in the support of the overlap distribution. We also show that the relevant critical points are pairwise orthogonal for two different low temperatures. This allows us to explain why temperature chaos occurs for those models, in contrast to the pure spherical models.