Generalized Random Energy Models in a Transversal Magnetic Field: Free Energy and Phase Diagrams

TL;DR

This paper derives explicit formulas for the free energy and phase diagrams of mean-field spin glasses with hierarchical interactions in a transverse magnetic field, revealing complex glass and magnetic transition behaviors.

Contribution

It provides the first explicit variational expressions for the free energy of GREM-like models in a transverse field, extending understanding of quantum spin glasses.

Findings

Explicit variational formulas for free energy

Detailed phase diagrams with glass and magnetic transitions

Analysis of the influence of the transverse field on glass phases

Abstract

We determine explicit variational expressions for the free energy of mean-field spin glasses in a transversal magnetic field, whose glass interaction is given by a hierarchical Gaussian potential as in Derrida's Generalized Random Energy Model (GREM), its continuous version (CREM) or the non-hierarchical GREM. The corresponding phase diagrams, which generally include glass transitions as well as magnetic transitions, are discussed. In the glass phase, the free energy is generally determined by both the parameters of the classical model and the transversal field.