Thermodynamics and universality for mean field quantum spin glasses

DOI10.1007/s00220-007-0263-xzbMath1138.82003arXivmath-ph/0610031OpenAlexW3099773826MaRDI QIDQ2472473

Nicholas Crawford

Publication date: 22 February 2008

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0610031

zbMATH Keywords

universalityspin-glassmean fieldthermodynamicquantum spin glass

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) (82D30) Quantum equilibrium statistical mechanics (general) (82B10)

Related Items (16)

General properties of overlap operators in disordered quantum spin systems ⋮ Generalized random energy models in a transversal magnetic field: free energy and phase diagrams ⋮ The free energy of a quantum Sherrington-Kirkpatrick spin-glass model for weak disorder ⋮ Universal nature of replica symmetry breaking in quantum systems with Gaussian disorder ⋮ Free energy subadditivity for symmetric random Hamiltonians ⋮ Spectral analysis of the quantum random energy model ⋮ Phase diagram of the quantum random energy model ⋮ Universality of replica-symmetry breaking in the transverse field Sherrington-Kirkpatrick model ⋮ Gauge theory for quantum XYZ spin glasses ⋮ Free energy of the quantum Sherrington–Kirkpatrick spin-glass model with transverse field ⋮ The quantum random energy model as a limit of p-spin interactions ⋮ Absence of replica symmetry breaking in the transverse and longitudinal random field Ising model ⋮ Approach to equilibrium for a class of random quantum models of infinite range ⋮ Zero-variance of perturbation Hamiltonian density in perturbed spin systems ⋮ Self-averaging of perturbation Hamiltonian density in perturbed spin systems ⋮ The de Almeida-Thouless line in hierarchical quantum spin glasses

Cites Work

• Structural properties of the disordered spherical and other mean field spin models
• Geometric aspects of quantum spin states
• The thermodynamic limit in mean field spin glass models
• Broken replica symmetry bounds in the mean field spin glass model
• Universality in Sherrington-Kirkpatrick's spin glass model
• The Parisi formula
• Existence of phase transitions for quantum lattice systems
• PROBABILISTIC DERIVATION OF A NONCOMMUTATIVE VERSION OF VARADHAN'S THEOREM
• Martingale Transforms
• THE THERMODYNAMIC LIMIT FOR FINITE DIMENSIONAL CLASSICAL AND QUANTUM DISORDERED SYSTEMS
• FREE ENERGY IN THE GENERALIZED SHERRINGTON–KIRKPATRICK MEAN FIELD MODEL
• Are there incongruent ground states in 2D Edwards-Anderson spin glasses?
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