Generalized Random Energy Models in a Transversal Magnetic Field: Free Energy and Phase Diagrams
Mathematical Physics
2022-07-20 v1 Disordered Systems and Neural Networks
math.MP
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.
Keywords
Cite
@article{arxiv.2007.03290,
title = {Generalized Random Energy Models in a Transversal Magnetic Field: Free Energy and Phase Diagrams},
author = {Chokri Manai and Simone Warzel},
journal= {arXiv preprint arXiv:2007.03290},
year = {2022}
}