On \(q\)-component models on Cayley tree: contour method

DOI10.1007/S11005-004-5117-2zbMath1076.82509OpenAlexW2027319878MaRDI QIDQ2571638

Utkir A. Rozikov

Publication date: 14 November 2005

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-004-5117-2

zbMATH Keywords

contourconfigurationCayley treeGibbs measurePotts modelSOS model

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 (16)

On contour arguments for the three state Potts model with competing interactions on a semi-infinite Cayley tree ⋮ Counting contours on trees ⋮ Gibbs measures for the three-state SOS model with external field on a Cayley tree ⋮ Ground states and Gibbs measures of Ising model with competing interactions and an external field on a Cayley tree ⋮ PIROGOV–SINAI THEORY WITH NEW CONTOURS FOR SYMMETRIC MODELS ⋮ Non-translation-invariant Gibbs measures of an SOS model on a Cayley tree ⋮ GIBBS MEASURES ON CAYLEY TREES: RESULTS AND OPEN PROBLEMS ⋮ Potts model with competing interactions on the Cayley tree: The contour method ⋮ A contour method on Cayley trees ⋮ A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree ⋮ Unnamed Item ⋮ Onq-component models on the Cayley tree: the general case ⋮ Ground states for the Potts model with competing interactions and a countable set of spin values on a Cayley tree ⋮ Phase diagrams of multicomponent lattice models ⋮ 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

• 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
• Random surfaces with two-sided constraints: An application of the theory of dominant ground states
• On the purity of the limiting Gibbs state for the Ising model on the Bethe lattice.
• On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras
• On Pure Phases of the Ising Model on the Bethe Lattices
• On Ising's model of ferromagnetism

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