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

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.

References in corpus (5)

• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Simple Glass Models and their Quantum Annealing
• Thermodynamics and Universality for Mean Field Quantum Spin Glasses
• Phase diagram of the $p$-spin-interacting spin glass with ferromagnetic bias and a transverse field in the infinite-$p$ limit
• Phase Diagram of the Quantum Random Energy Model

Cited by in corpus (3)

• Spectral Analysis of the Quantum Random Energy Model
• The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses
• Generalized Random Energy Models in a Transversal Magnetic Field: Free Energy and Phase Diagrams