Potts model with competing interactions on the Cayley tree: The contour method

DOI10.1007/S11232-007-0125-XzbMath1157.82308OpenAlexW2019102097MaRDI QIDQ2480103

Utkir A. Rozikov, Golibjon Isroilovich Botirov

Publication date: 31 March 2008

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

Full work available at URL: https://doi.org/10.1007/s11232-007-0125-x

zbMATH Keywords

ground stateconfigurationCayley treeGibbs measurecontour method

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

Related Items (17)

On ground states and phase transition for \(\lambda\)-model with the competing Potts interactions on Cayley trees ⋮ Periodic ground states for the Potts model with external field and a countable set of spin values on the Cayley tree ⋮ Periodic and weakly periodic ground states for the Potts model with competing interactions on the Cayley tree ⋮ Ground states and Gibbs measures of Ising model with competing interactions and an external field on a Cayley tree ⋮ Gibbs measures of the Blume-Emery-Griffiths model on the Cayley tree ⋮ Weakly periodic ground states for the \(\lambda \)-model ⋮ Weakly periodic Gibbs measures and ground states for the Potts model with competing interactions on the Cayley tree ⋮ GIBBS MEASURES ON CAYLEY TREES: RESULTS AND OPEN PROBLEMS ⋮ New classes of ground states for the Potts model with random competing interactions on a Cayley tree ⋮ Unnamed Item ⋮ Gibbs measures for the Potts model with a countable set of spin values on a Cayley tree ⋮ Description of weakly periodic ground states for the Potts model with external field and a countable set of spin values on a Cayley tree ⋮ Ground states and Gibbs measures for the Potts-SOS model with an external field on the Cayley tree ⋮ Ground states of Ising-Potts model on Cayley tree ⋮ Ground states for the Potts model with an external field ⋮ Ground states for the Potts model with competing interactions and a countable set of spin values on a Cayley tree ⋮ Gibbs measures of Potts model on Cayley trees: A survey and applications

Cites Work

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• A hard-core model on a Cayley tree: an example of a loss network
• 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 Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras
• A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree
• On \(q\)-component models on Cayley tree: contour method
• On Pure Phases of the Ising Model on the Bethe Lattices
• On Ising's model of ferromagnetism

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