Universal structures in some mean field spin glasses, and an application

TL;DR

This paper explores a spin glass model similar to the Random Energy Model, providing new insights into the Parisi minimization and demonstrating complex phenomena like ultrametricity and temperature chaos through an application involving an extensive cavity field.

Contribution

It introduces a spin glass model that simplifies the Parisi minimization and reveals its physical meaning, with an application showing complex behaviors in Derrida's REM.

Findings

Recasting Parisi minimization as a Gibbs variational principle

Demonstrating ultrametricity in the model

Observing chaos in temperature in the applied model

Abstract

We discuss a spin glass reminiscent of the Random Energy Model, which allows in particular to recast the Parisi minimization into a more classical Gibbs variational principle, thereby shedding some light on the physical meaning of the order parameter of the Parisi theory. As an application, we study the impact of an extensive cavity field on Derrida's REM: Despite its simplicity, this model displays some interesting features such as ultrametricity and chaos in temperature.