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Description of all translation-invariant $$p$$-adic Gibbs measures for the Potts model on a Cayley tree. (English) Zbl 1332.82018
$$p$$-adic numbers $$Q_p$$ are more and more used to revise theoretical and mathematical physics and the present paper is in this trend. The main result herein is the characterization and the counting of TIpGMs (translation-invariant $$p$$-adic Gibbs measure). The analysis is based on the tree recession for boundary fields, the fixed points of which are characterizing the TIpGMs.

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