Absence of Dobrushin states for \(2d\) long-range Ising models

DOI10.1007/s10955-018-2097-7zbMath1401.82004arXiv1804.04889OpenAlexW2798093803MaRDI QIDQ1990101

Aernout C. D. van Enter, Loren Coquille, Arnaud Le Ny, Wioletta M. Ruszel

Publication date: 24 October 2018

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

Full work available at URL: https://arxiv.org/abs/1804.04889

zbMATH Keywords

Gibbs statesinterface fluctuationsDobrushin stateslong-range Ising model

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (5)

Decimations for two-dimensional Ising and rotator models ⋮ Existence of gradient Gibbs measures on regular trees which are not translation invariant ⋮ One-Sided Versus Two-Sided Stochastic Descriptions ⋮ The roles of random boundary conditions in spin systems ⋮ Nucleation for one-dimensional long-range Ising models

Cites Work

• A finite-volume version of Aizenman-Higuchi theorem for the 2D Ising model
• Gibbs measures and phase transitions.
• Generalized classical theory of magnetism
• Non-translation invariant Gibbs states with coexisting phases. I: Existence of sharp interface for Widom-Rowlinson type lattice models in three dimensions
• Absence of crystalline ordering in two dimensions
• One dimensional spin glasses with potential decay \(1/r^{1+\epsilon}\). Absence of phase transitions and cluster properties
• Examples of DLR states which are not weak limits of finite volume Gibbs measures with deterministic boundary conditions
• Gibbs State Describing Coexistence of Phases for a Three-Dimensional Ising Model
• Statistical Mechanics of Lattice Systems
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