The de Almeida-Thouless Line in Hierarchical Quantum Spin Glasses

Abstract

We determine explicitly and discuss in detail the effects of the joint presence of a longitudinal and a transversal (random) magnetic field on the phases of the Random Energy Model (REM) and its hierarchical generalization, the GREM. Our results extent known results both in the classical case of vanishing transversal field and in the quantum case for vanishing longitudinal field. Following Derrida and Gardner, we argue that the longitudinal field has to be implemented hierarchically also in the Quantum GREM. We show that this ensures the shrinking of the spin glass phase in the presence of the magnetic fields as also expected for the Quantum Sherrington-Kirkpatrick model.

32 pages, 3 figures

References in corpus (6)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Stability of the quantum Sherrington-Kirkpatrick spin glass model
• 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
• Dynamical Approach to the TAP Equations for the Sherrington-Kirkpatrick Model

Cited by in corpus (5)

• A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model
• Spectral Analysis of the Quantum Random Energy Model
• Equilibrium dynamics of infinite-range quantum spin glasses in a field
• Spin-glass quantum phase transition in amorphous arrays of Rydberg atoms
• Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model