Absence of phase transitions in one-dimensional antiferromagnetic models with long-range interactions

DOI10.1007/BF01048025zbMath1100.82507MaRDI QIDQ2499878

Azer Kerimov

Publication date: 23 August 2006

Published in: Journal of Statistical Physics (Search for Journal in Brave)

zbMATH Keywords

Hamiltonianground stateGibbs stateextreme Gibbs stateinteracting and noninteracting contours

Mathematics Subject Classification ID

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

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ONE-DIMENSIONAL NON-SYMMETRIC WIDOM–ROWLINSON MODEL WITH LONG-RANGE INTERACTION ⋮ ONE-DIMENSIONAL LONG-RANGE FERROMAGNETIC ISING MODEL UNDER WEAK AND SPARSE EXTERNAL FIELD ⋮ PHASE DIAGRAMS OF ONE-DIMENSIONAL MODELS UNDER STRONG RANDOM EXTERNAL FIELD ⋮ Hydrodynamics and transport in the long-range-interacting φ ⁴ chain ⋮ Quasi-additive estimates on the Hamiltonian for the one-dimensional long range Ising model ⋮ Ground state criteria in one-dimensional antiferromagnetic Ising model with long range interaction ⋮ A disagreement-percolation type uniqueness condition for Gibbs states in models with long-range interactions ⋮ Mean-field driven first-order phase transitions in systems with long-range interactions ⋮ A Class of One-Dimensional Models with Unique Ground States that Admits Phase Transitions ⋮ Uniqueness of Gibbs states in one-dimensional antiferromagnetic model with long-range interaction

Cites Work

• First order phase transitions in lattice and continuous systems: Extension of Pirogov-Sinai theory
• Interface sharpness in the Ising model with long-range interaction.
• Existence of a phase-transition in a one-dimensional Ising ferromagnet
• Statistical mechanics of a one-dimensional lattice gas