Positive fixed points of quadratic operators and Gibbs measures

DOI10.1007/s11117-015-0394-9zbMath1354.82005OpenAlexW2237151815MaRDI QIDQ346424

Yusup Khalbaevich Eshkabilov, Farhod Halimjonovich Haydarov, Shohruh Dilmurodovich Nodirov

Publication date: 29 November 2016

Published in: Positivity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11117-015-0394-9

zbMATH Keywords

fixed pointconfigurationCayley treequadratic operatortranslational-invariant Gibbs measure

Mathematics Subject Classification ID

Trees (05C05) 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 (7)

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 ⋮ 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 ⋮ Positive Fixed Points of Cubic Operators on R² and Gibbs Measures

Cites Work

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• Countable state space Markov random fields and Markov chains on trees
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• Markov random fields on an infinite tree
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• On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice.
• Phase transition and critical values of a nearest-neighbor system with uncountable local state space on Cayley trees
• 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
• Periodic Gibbs measures for models with uncountable set of spin values on a Cayley tree

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