Free energy and complexity of spherical bipartite models

TL;DR

This paper analyzes the free energy and complexity of spherical bipartite spin glass models, providing a variational formula at high temperature and bounds on the ground state energy, revealing exponential growth in local minima at low energy levels.

Contribution

It introduces a variational formula for free energy in spherical bipartite models and bounds the ground state energy, advancing understanding of their energy landscape.

Findings

Derived a high-temperature variational formula for free energy.

Showed the number of local minima grows exponentially at low energy.

Provided bounds on the ground state energy location.

Abstract

We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti-Sommers representation of the mixed p-spin spherical model. Next, we show that the mean number of local minima at low levels of energy is exponentially large in the size of the system and we derive a bound on the location of the ground state energy.