The de Almeida–Thouless Line in Hierarchical Quantum Spin Glasses

Chokri Manai, Simone Warzel

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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 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 is also expected for the Quantum Sherrington–Kirkpatrick model.

Original languageEnglish
Article number14
JournalJournal of Statistical Physics
Issue number1
StatePublished - Jan 2022


  • Disordered systems
  • Free energy
  • Phase transition
  • Quantum spin glass


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