Weakly periodic Gibbs measures of the Ising model with an external field on the Cayley tree

DOI10.1007/s11232-015-0298-7zbMath1327.82019OpenAlexW2172553816MaRDI QIDQ499419

Muzaffar Rahmatullaev

Publication date: 30 September 2015

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

Full work available at URL: https://doi.org/10.1007/s11232-015-0298-7

zbMATH Keywords

Cayley treeGibbs measureweakly periodic measureIsing model with external field

Mathematics Subject Classification ID

Trees (05C05) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Statistical mechanics of magnetic materials (82D40)

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Weakly periodic Gibbs measures of the Ising model on the Cayley tree of order five and six ⋮ Periodic Gibbs measures for the Potts-SOS model on a Cayley tree ⋮ Weakly periodic Gibbs measures for the Ising model on the Cayley tree of order \(k=2\)

Cites Work

• Countable state space Markov random fields and Markov chains on trees
• Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree
• A description of harmonic functions via properties of the group representation of the Cayley tree.
• Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree
• Gibbs measures and phase transitions
• Markov random fields on an infinite tree
• Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model
• The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree
• Gibbs Measures on Cayley Trees
• On Pure Phases of the Ising Model on the Bethe Lattices
• Gibbs States on Countable Sets
• Quadratic transformations: a model for population growth. I

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