Phase transitions for a model with uncountable set of spin values on a Cayley tree

DOI10.1134/S1995080213030050zbMath1276.05060arXiv1210.7311OpenAlexW1986691258MaRDI QIDQ384228

Yusup Khalbaevich Eshkabilov, Utkir A. Rozikov, Golibjon Isroilovich Botirov

Publication date: 27 November 2013

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.7311

zbMATH Keywords

phase transitionsconfigurationCayley treeGibbs measures

Mathematics Subject Classification ID

Trees (05C05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (8)

Positive fixed points of quadratic operators and Gibbs measures ⋮ A model with uncountable set of spin values on a Cayley tree: phase transitions ⋮ Phase transitions for a model with uncountable spin space on the Cayley tree: the general case ⋮ Phase transitions for models with a continuum set of spin values on a Bethe lattice ⋮ Phase transition and critical values of a nearest-neighbor system with uncountable local state space on Cayley trees ⋮ Nontranslation invariant Gibbs measures for models with uncountable set of spin values on a Cayley tree ⋮ Anisotropic Ising Model with Countable Set of Spin Values on Cayley Tree ⋮ Positive Fixed Points of Cubic Operators on R² and Gibbs Measures

Cites Work

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• Markov random fields on an infinite tree
• Description of periodic extreme Gibbs measures of some lattice models on the Cayley tree
• 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
• On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice.
• The Potts model with countable set of spin values on a Cayley tree
• On Pure Phases of the Ising Model on the Bethe Lattices
• Gibbs States on Countable Sets

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