Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model

DOI10.1007/BF02557197zbMath0957.82007OpenAlexW2033484646MaRDI QIDQ1568022

Utkir A. Rozikov

Publication date: 26 June 2000

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02557197

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Stochastic methods applied to problems in equilibrium statistical mechanics (82B31)

Related Items (18)

Periodic Algebras Generated by Groups ⋮ Weakly periodic Gibbs measures of the Ising model on the Cayley tree of order five and six ⋮ Nonuniqueness of a Gibbs measure for a model on the Cayley tree ⋮ A description of harmonic functions via properties of the group representation of the Cayley tree. ⋮ Stability of the phase transition of critical-field Ising model on Cayley trees under inhomogeneous external fields ⋮ Periodic points of a \(p\)-adic operator and their \(p\)-adic Gibbs measures ⋮ New weakly periodic Gibbs measures of Ising model on Cayley tree ⋮ A Three State Hard-Core Model on a Cayley Tree ⋮ Weakly periodic Gibbs measures of the Ising model with an external field on the Cayley tree ⋮ Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree ⋮ Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree ⋮ GIBBS MEASURES ON CAYLEY TREES: RESULTS AND OPEN PROBLEMS ⋮ Nonuniqueness of a Gibbs measure for the Ising ball model ⋮ Weakly periodic Gibbs measures for the Ising model on the Cayley tree of order \(k=2\) ⋮ Fertile HC models with three states on a Cayley tree ⋮ On Ising model with four competing interactions on Cayley tree ⋮ Gibbs measures for the SOS model with four states on a Cayley tree ⋮ Gibbs measures of Potts model on Cayley trees: A survey and applications

Cites Work

• Extremity of the disordered phase in the Ising model on the Bethe lattice
• 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 Pure Phases of the Ising Model on the Bethe Lattices
• Gibbs States on Countable Sets

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