Geodesic
Anisotropic Ising model with countable set of spin values on Cayley tree
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 305-309.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we investigate of an infinite system of functional equations for the Ising model with competing interactions and countable spin values $0,1,\ldots$ and non zero filed on a Cayley tree of order two. We derived an infinite system of functional equations for the Ising model that is we describe conditions on $h_x$ guaranteeing compatibility of distributions $\mu^{(n)}(\sigma_n)$.
Keywords: Cayley tree, Ising model, Gibbs measures, functional equations, compatibility of distributions measures. 
@article{JSFU_2017_10_3_a5,
     author = {Golibjon I. Botirov},
     title = {Anisotropic {Ising} model with countable set of spin values on {Cayley} tree},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {305--309},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a5/}
}
TY  - JOUR
AU  - Golibjon I. Botirov
TI  - Anisotropic Ising model with countable set of spin values on Cayley tree
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2017
SP  - 305
EP  - 309
VL  - 10
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a5/
LA  - en
ID  - JSFU_2017_10_3_a5
ER  - 
%0 Journal Article
%A Golibjon I. Botirov
%T Anisotropic Ising model with countable set of spin values on Cayley tree
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2017
%P 305-309
%V 10
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a5/
%G en
%F JSFU_2017_10_3_a5
Golibjon I. Botirov. Anisotropic Ising model with countable set of spin values on Cayley tree. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 305-309. http://geodesic.mathdoc.fr/item/JSFU_2017_10_3_a5/

[1] S. Katsura, M. Takizawa, “Bethe lattice and the Bethe approximation”, Prog. Theor. Phys., 51 (1974), 82–98 | DOI

[2] E. Mueller-Hartmann, “Theory of the Ising model on a Cayley tree”, J. Phys. B, 27 (1977), 161–168

[3] C. Preston, Gibbs States on countabel sets, Cambridge Uni. Press, London, 1974 | MR

[4] N. N. Ganikhodjaev, “The Potts model on $Z^d$ eith countable set of spin values”, J. Math. Phys., 45 (2004), 1121–1127 | DOI | MR | Zbl

[5] N. N. Ganikhodjaev, U. A. Rozikov, “The Potts model with countable set of spin values on a Cayley tree”, Letters in Math. Phys., 75 (2006), 99–109 | DOI | MR | Zbl

[6] Yu. Kh. Eshkabilov, U. A. Rozikov, G. I. Botirov, “Phase transition for a model with uncountable set of spin values on Cayley tree”, Lobachevskii Journal of Mathematics, 34:3 (2013), 256–263 | DOI | MR | Zbl

[7] Yu. Kh. Eshkobilov, F. H. Haydarov, U. A. Rozikov, “Non-uniqueness of Gibbs Measure for Models with Uncountable Set of Spin Values on a Cayley Tree”, Jour. Stat. Phys., 147:4 (2012), 779–794 | DOI | MR