Vol. 3, No. 2, 2022

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Generalized random energy models in a transversal magnetic field: Free energy and phase diagrams

Chokri Manai and Simone Warzel

Vol. 3 (2022), No. 2, 215–245
Abstract

We determine explicit variational expressions for the quantum 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 nonhierarchical GREM. The corresponding phase diagrams, which generally include glass transitions as well as transitions to quantum paramagnetic and mixed quantum-classical phases, are discussed. In the glass phase, the free energy is generally determined by both the parameters of the classical model and the transversal field.

Keywords
quantum spin glass, phase transition, free energy
Mathematical Subject Classification
Primary: 82B44, 82D30
Milestones
Received: 15 July 2020
Accepted: 27 June 2021
Published: 8 July 2022
Authors
Chokri Manai
Zentrum Mathematik
Technische Universität München
Garching bei München
Germany
Simone Warzel
Zentrum Mathematik
Technische Universität München
Garching bei München
Germany