Geodesic
Gibbs measures for the Potts model with a countable set of spin values on a Cayley tree
Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 2, pp. 318-328
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We consider an infinite system of functional equations for the Potts model with competing interactions of radius $r=2$ and countable spin values $\Phi=\{0,1,\ldots,\}$ on the Cayley tree of order $k=2$. We reduce the problem to the description of the solutions of some infinite system of equations for any $k=2$ and any fixed probability measure $\nu$ with $\nu(i)>0$ on the set of all nonnegative integer numbers. We also give a description of the class of measures $\nu$ on $\Phi$ such that the infinite system of equations has unique solution $\{a^i,\,i=1,2,\ldots\}$, $a\in(0,1)$, with respect to each element of this class.
Keywords: Cayley tree, Potts model, Gibbs measure, functional equation. 
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     title = {Gibbs measures for {the~Potts} model with a~countable set of spin values on {a~Cayley} tree},
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G. I. Botirov; Z. E. Mustafoeva. Gibbs measures for the Potts model with a countable set of spin values on a Cayley tree. Teoretičeskaâ i matematičeskaâ fizika, Tome 214 (2023) no. 2, pp. 318-328. http://geodesic.mathdoc.fr/item/TMF_2023_214_2_a10/

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