Translation-invariant Gibbs measures for a model with logarithmic potential on a Cayley tree
https://doi.org/10.17586/2220-8054-2016-7-5-893-899
Abstract
In this paper, we consider a model with logarithmical potential and with the set [0, 1] of spin values, on a Cayley tree Гk 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.
About the Authors
Yu. Kh. Eshkabilov
National University of Uzbekistan
Uzbekistan
Uzbekistan
Tashkent
Sh. P. Bobonazarov
Tashkent Institute of Irrigation and Melioration
Uzbekistan
Uzbekistan
Tashkent
R. I. Teshaboev
Termez State University
Uzbekistan
Uzbekistan
Termez
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Review
For citations:
Eshkabilov Yu.Kh., Bobonazarov Sh.P., Teshaboev R.I. Translation-invariant Gibbs measures for a model with logarithmic potential on a Cayley tree. Nanosystems: Physics, Chemistry, Mathematics. 2016;7(5):893-899. https://doi.org/10.17586/2220-8054-2016-7-5-893-899
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