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

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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. 
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     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/}
}
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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/