The Quantum Random Energy Model as a Limit of p-Spin Interactions

TL;DR

This paper demonstrates that the free energy of a mean-field quantum spin glass with p-spin interactions converges to that of the quantum random energy model as p approaches infinity, linking finite p models to the QREM.

Contribution

It establishes the convergence of the free energy of p-spin models to the QREM in a joint thermodynamic and p to infinity limit, providing a rigorous connection between these models.

Findings

Convergence of free energy as p approaches infinity

Rigorous link between p-spin models and QREM

Validation of QREM as a limit case

Abstract

We consider the free energy of a mean-field quantum spin glass described by a $ p $-spin interaction and a transversal magnetic field. Recent rigorous results for the case $ p= \infty $, i.e. the quantum random energy model (QREM), are reviewed. We show that the free energy of the $ p $-spin model converges in a joint thermodynamic and $ p \to \infty $ limit to the free energy of the QREM.