Periodic Gibbs measures for models with uncountable set of spin values on a Cayley tree

DOI10.1142/S021902571550006XzbMath1311.82005arXiv1302.6055OpenAlexW2963407943MaRDI QIDQ5247188

Farhod Halimjonovich Haydarov, Utkir A. Rozikov

Publication date: 23 April 2015

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.6055

zbMATH Keywords

existenceconfigurationCayley treeGibbs measuresnon existence

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Classical equilibrium statistical mechanics (general) (82B05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (9)

Positive fixed points of quadratic operators and Gibbs measures ⋮ Four competing interactions for models with an uncountable set of spin values on a Cayley tree ⋮ Phase transitions for models with a continuum set of spin values on a Bethe lattice ⋮ Uniqueness of Gibbs measures for an Ising model with continuous spin values on a Cayley tree ⋮ New condition on uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree ⋮ On normal subgroups of the group representation of the Cayley tree ⋮ Nontranslation invariant Gibbs measures for models with uncountable set of spin values on a Cayley tree ⋮ Positive Fixed Points of Cubic Operators on R² and Gibbs Measures ⋮ Invariance property on group representations of the Cayley tree and its applications

Cites Work

• Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree
• On models with uncountable set of spin values on a Cayley tree: integral equations
• Non-uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree
• Gibbs measures and phase transitions.
• Partition structures of the group representation of the Cayley tree into cosets by finite-index normal subgroups and their applications to the description of periodic Gibbs distributions
• Robust phase transitions for Heisenberg and other models on general trees
• ESTABLISHMENT AND FECUNDITY IN SPATIAL ECOLOGICAL MODELS: STATISTICAL APPROACH AND KINETIC EQUATIONS
• Gibbs Measures on Cayley Trees

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