Periodic Gibbs measures for the Potts model on the Cayley tree

DOI10.1007/s11232-013-0055-8zbMath1286.82006OpenAlexW2039895629MaRDI QIDQ2449488

R. M. Khakimov, Utkir A. Rozikov

Publication date: 8 May 2014

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

Full work available at URL: https://doi.org/10.1007/s11232-013-0055-8

zbMATH Keywords

configurationCayley treeGibbs measurePotts modeltranslation-invariant measureperiodic measure

Mathematics Subject Classification ID

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

Related Items (19)

Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree ⋮ On ground states and phase transition for \(\lambda\)-model with the competing Potts interactions on Cayley trees ⋮ Unnamed Item ⋮ Periodic Gibbs measures for the Potts model in translation-invariant and periodic external fields on the Cayley tree ⋮ On $(k_0)$-translation-invariant and $(k_0)$-periodic Gibbs measures for Potts model on Cayley tree ⋮ Potts model on a Cayley tree: a new class of Gibbs measures ⋮ Periodic ground states for the mixed spin Ising model with competing interactions on a Cayley tree ⋮ Localization of translation-invariant Gibbs measures for the Potts and ``solid-on-solid models on a Cayley tree ⋮ Phase transition and chaos: \(p\)-adic Potts model on a Cayley tree ⋮ Free energies of the Potts model on a Cayley tree ⋮ Periodic \(p\)-adic Gibbs measures of \(q\)-state Potts model on Cayley trees. I: The chaos implies the vastness of the set of \(p\)-adic Gibbs measures ⋮ Periodic Gibbs measures for the Potts-SOS model on a Cayley tree ⋮ Translation invariance of the periodic Gibbs measures for the Potts model on the Cayley tree ⋮ Ground states and phase transition of the \(\lambda\) model on the Cayley tree ⋮ A weakly periodic Gibbs measure for the ferromagnetic Potts model on a Cayley tree ⋮ Extremality of translation-invariant Gibbs measures for the Potts–SOS model on the Cayley tree ⋮ On the constructive description of Gibbs measures for the Potts model on a Cayley tree ⋮ Periodic and weakly periodic ground states corresponding to subgroups of index three for the Ising model on Cayley tree ⋮ Gibbs measures of Potts model on Cayley trees: A survey and applications

Cites Work

• Metastability in the Potts model on the Cayley tree
• Description of periodic extreme Gibbs measures of some lattice models on the Cayley tree
• The Potts model with countable set of spin values on a Cayley tree
• Gibbs States on Countable Sets
• New order parameters in the Potts model on a Cayley tree
• A Three State Hard-Core Model on a Cayley Tree

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