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

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.

References in corpus (7)

• Many-body mobility edge in a mean-field quantum spin glass
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• Existence of replica-symmetry breaking in quantum glasses
• Phase diagram of the $p$-spin-interacting spin glass with ferromagnetic bias and a transverse field in the infinite-$p$ limit
• On a nonhierarchical version of the generalized random energy model
• The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses

Cited by in corpus (3)

• Spectral Analysis of the Quantum Random Energy Model
• The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses
• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model