On free energy of non-convex multi-species spin glasses

TL;DR

This paper extends the understanding of free energy limits in non-convex multi-species spin glass models, showing that if the limit exists, it must be a critical point of a specific functional, even with complex species interactions.

Contribution

It generalizes previous results to multi-species models with non-convex interactions, addressing challenges from irrational species proportions and non-approximability.

Findings

If the free energy limit exists, it is a critical value of a certain functional.

The work extends the critical point characterization to multi-species models with complex interactions.

Addresses the non-approximability issue due to irrational species proportions.

Abstract

In [arXiv:2311.08980], it was shown that if the limit of the free energy in a non-convex vector spin glass model exists, it must be a critical value of a certain functional. In this work, we extend this result to multi-species spin glass models with non-convex interactions, where spins from different species may lie in distinct vector spaces. Since the species proportions may be irrational and the existence of the limit of the free energy is not generally known, non-convex multi-species models cannot be approximated by vector spin models in a straightforward manner, necessitating more careful treatment.