A QUANTUM CRYSTAL MODEL IN THE LIGHT-MASS LIMIT: GIBBS STATES

DOI10.1142/S0129055X00000381zbMath0976.82010OpenAlexW1971932859MaRDI QIDQ4519861

André F. Verbeure, Robert Adol'fovich Minlos, Valentin A. Zagrebnov

Publication date: 4 December 2000

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

Full work available at URL: https://doi.org/10.1142/s0129055x00000381

zbMATH Keywords

partition functionsquasilocal algebracluster expansionsquantum Gibbs statesferroelectric anharmonic quantum oscillatorFeynman-Kac-Nelson representationlight-mass rescaling

Mathematics Subject Classification ID

Quantum equilibrium statistical mechanics (general) (82B10) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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Cites Work

• Perturbations of Gibbs semigroups
• Stochastic processes associated with KMS states
• Homogeneous random fields and statistical mechanics
• Suppression of critical fluctuations by strong quantum effects in quantum lattice systems
• Uniqueness of Gibbs states for quantum lattice systems
• Phase transitions and algebra of fluctuation operators in an exactly soluble model of a quantum anharmonic crystal
• Uniqueness and clustering properties of Gibbs states for classical and quantum unbounded spin systems.
• Peierls argument and long-range order behavior of quantum lattice systems with unbounded spins
• Small-mass behavior of quantum Gibbs states for lattice models with unbounded spins
• Dynamics of quantum fluctuations in an anharmonic crystal model
• No-go theorem for quantum structural phase transitions

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