Geodesic
Translation-invariant Gibbs measures for a model with logarithmic potential on a Cayley tree
Nanosistemy: fizika, himiâ, matematika, Tome 7 (2016) no. 5, pp. 893-899

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In this paper, we consider a model with logarithmical potential and with the set [0, 1] of spin values, on a Cayley tree $\Gamma^k$ of the order $k$. In the case $k= 2;3$, we shall prove that, there is a unique translation-invariant splitting Gibbs measure for this model. For the case $k=4$, we show that there are three translation-invariant Gibbs measures for this model.
Keywords: Cayley tree, translation-invariant Gibbs measure, fixed point, nonlinear operator.
Mots-clés : configuration 
@article{NANO_2016_7_5_a11,
     author = {Yu. Kh. Eshkabilov and Sh. P. Bobonazarov and R. I. Teshaboev},
     title = {Translation-invariant {Gibbs} measures for a model with logarithmic potential on a {Cayley} tree},
     journal = {Nanosistemy: fizika, himi\^a, matematika},
     pages = {893--899},
     publisher = {mathdoc},
     volume = {7},
     number = {5},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/NANO_2016_7_5_a11/}
}
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Yu. Kh. Eshkabilov; Sh. P. Bobonazarov; R. I. Teshaboev. Translation-invariant Gibbs measures for a model with logarithmic potential on a Cayley tree. Nanosistemy: fizika, himiâ, matematika, Tome 7 (2016) no. 5, pp. 893-899. http://geodesic.mathdoc.fr/item/NANO_2016_7_5_a11/