Uniqueness of Gibbs measure for models with uncountable set of spin values on a Cayley tree

DOI10.1007/s11040-012-9118-6zbMath1277.82008arXiv1202.1722OpenAlexW2077128609MaRDI QIDQ360219

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

Publication date: 26 August 2013

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.1722

zbMATH Keywords

uniquenessconfigurationCayley treeGibbs measures

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 (11)

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 ⋮ Non-uniqueness of Gibbs measure for models with 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 ⋮ 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 ⋮ Existence and uniqueness of fixed points of an integral operator of Hammerstein type ⋮ Periodic 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

Cites Work

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• 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.
• 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 disordered phase in the ferromagnetic Potts model on the Bethe lattice
• On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice.
• Robust phase transitions for Heisenberg and other models on general trees
• The Potts model with countable set of spin values on a Cayley tree
• No phase transition for Gaussian fields with bounded spins
• Periodic Gibbs measures of the inhomogeneous Ising model on trees
• On Pure Phases of the Ising Model on the Bethe Lattices
• Gibbs States on Countable Sets

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