Free energy upper bound for mean-field vector spin glasses

TL;DR

This paper establishes an upper bound for the free energy in mean-field vector spin glasses, using an infinite-dimensional Hamilton-Jacobi equation, advancing understanding of their thermodynamic limits.

Contribution

It introduces a novel upper bound for the free energy of vector spin glasses applicable to a broad class of models, formulated via an infinite-dimensional Hamilton-Jacobi equation.

Findings

Derived a sharp upper bound for the free energy.

Applicable to a wide class of vector spin glass models.

Bound expressed through an infinite-dimensional Hamilton-Jacobi equation.

Abstract

We consider vector spin glasses whose energy function is a Gaussian random field with covariance given in terms of the matrix of scalar products. For essentially any model in this class, we give an upper bound for the limit free energy, which is expected to be sharp. The bound is expressed in terms of an infinite-dimensional Hamilton-Jacobi equation.