Phase transition and chaos: \(p\)-adic Potts model on a Cayley tree

DOI10.1016/j.chaos.2016.04.003zbMath1355.37106OpenAlexW2337769052MaRDI QIDQ508252

Otabek Khakimov, Farrukh Mukhamedov

Publication date: 10 February 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2016.04.003

zbMATH Keywords

shift\(p\)-adic numbersPotts modelperiodic\(p\)-adic quasi Gibbs measure

Mathematics Subject Classification ID

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) Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) (37N20) Difference operators (39A70) Operator theory over fields other than (mathbb{R}), (mathbb{C}) or the quaternions; non-Archimedean operator theory (47S10)

Related Items (16)

Chaos in p-adic Statistical Lattice Models: Potts Model ⋮ Chaotic behavior of the p-adic Potts–Bethe mapping II ⋮ On Julia set and chaos in \(p\)-adic Ising model on the 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 \(p\)-adic Ising model in an external field on a Cayley tree: periodic Gibbs measures ⋮ The description of generalized translation-invariant \(p\)-adic Gibbs measures for the Potts model on the Cayley tree of order three ⋮ Ergodicity and periodic orbits of \(p\)-adic \((1,2)\)-rational dynamical systems with two fixed points ⋮ \(p\)-adic dynamical systems of (2,2)-rational functions with unique fixed point ⋮ p$$ p $$‐Adic phase transitions for countable state Potts model ⋮ \(p\)-adic dynamical systems of \((3,1)\)-rational functions with unique fixed point ⋮ Rational map \(ax + 1/x\) on the projective line over \(\mathbb{Q}_2\) ⋮ 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 periodic \(p\)-adic generalized Gibbs measures for Ising model on a Cayley tree ⋮ Gibbs measures of Potts model on Cayley trees: A survey and applications

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