Description of all translation-invariant $p$-adic Gibbs measures for the Potts model on a Cayley tree

zbMath1332.82018arXiv1402.6150MaRDI QIDQ5500153

Utkir A. Rozikov, Otabek Khakimov

Publication date: 5 August 2015

Full work available at URL: https://arxiv.org/abs/1402.6150

zbMATH Keywords

Cayley tree\(p\)-adic number\(p\)-adic Gibbs measure\(p\)-adic Potts model

Mathematics Subject Classification ID

Trees (05C05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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Chaos in p-adic Statistical Lattice Models: Potts Model ⋮ Chaotic behavior of the p-adic Potts–Bethe mapping II ⋮ On periodic Gibbs measures of \(p\)-adic Potts model on a Cayley tree ⋮ Chaotic behavior of the \(p\)-adic Potts-Bethe mapping ⋮ Dynamical systems of the \(p\)-adic (2, 2)-rational functions with two fixed points ⋮ The description of generalized translation-invariant \(p\)-adic Gibbs measures for the Potts model on the Cayley tree of order three ⋮ \(p\)-adic dynamical systems of (2,2)-rational functions with unique fixed point ⋮ \(p\)-adic solid-on-solid model on a Cayley tree ⋮ Phase transition and chaos: \(p\)-adic Potts model on a Cayley tree ⋮ Local descriptions of roots of cubic equations over \(p\)-adic fields ⋮ 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 ⋮ On \(G_2\)-periodic quasi Gibbs measures of \(p\)-adic Potts model on a Cayley tree ⋮ On descriptions of all translation invariant \(p\)-adic Gibbs measures for the Potts model on the Cayley tree of order three

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