Non-uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree

DOI10.1007/s10955-012-0494-xzbMath1252.82026arXiv1202.2542OpenAlexW3103497304MaRDI QIDQ438767

Farhod Halimjonovich Haydarov, Utkir A. Rozikov, Yusup Khalbaevich Eshkabilov

Publication date: 31 July 2012

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

Full work available at URL: https://arxiv.org/abs/1202.2542

zbMATH Keywords

uniquenessconfigurationCayley treeGibbs measures

Mathematics Subject Classification ID

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

Related Items (16)

On the set of Gibbs measures for model with a countable set of spin values on Cayley trees ⋮ Mirror symmetry of height-periodic gradient Gibbs measures of an SOS model on Cayley trees ⋮ Positive fixed points of quadratic operators and Gibbs measures ⋮ Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree ⋮ Four competing interactions for models with an uncountable set of spin values on a Cayley tree ⋮ Phase transitions for a model with uncountable set of spin values on a Cayley tree ⋮ 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 ⋮ GIBBS MEASURES ON CAYLEY TREES: RESULTS AND OPEN PROBLEMS ⋮ Phase transition and critical values of a nearest-neighbor system with uncountable local state space on Cayley trees ⋮ Fixed points of Lyapunov integral operators and Gibbs measures ⋮ Nontranslation invariant Gibbs measures for models with uncountable set of spin values on a Cayley tree ⋮ Periodic 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

• 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
• Countable state space Markov random fields and Markov chains on trees
• A hard-core model on a Cayley tree: an example of a loss network
• On Ising model with four competing interactions on Cayley tree
• 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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