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.
@article{TMF_2023_214_2_a10,
author = {G. I. Botirov and Z. E. Mustafoeva},
title = {Gibbs measures for {the~Potts} model with a~countable set of spin values on {a~Cayley} tree},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {318--328},
publisher = {mathdoc},
volume = {214},
number = {2},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2023_214_2_a10/}
}
TY - JOUR AU - G. I. Botirov AU - Z. E. Mustafoeva TI - Gibbs measures for the~Potts model with a~countable set of spin values on a~Cayley tree JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2023 SP - 318 EP - 328 VL - 214 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2023_214_2_a10/ LA - ru ID - TMF_2023_214_2_a10 ER -
%0 Journal Article %A G. I. Botirov %A Z. E. Mustafoeva %T Gibbs measures for the~Potts model with a~countable set of spin values on a~Cayley tree %J Teoretičeskaâ i matematičeskaâ fizika %D 2023 %P 318-328 %V 214 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2023_214_2_a10/ %G ru %F TMF_2023_214_2_a10
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/