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Scientific Bulletin of Namangan State University

Abstract

In this paper under some conditions on parametres of the three states Potts model on the Cayley tree of order three it is proved existence of the periodic Gibbs measures and is showed that the number of these measures is three.

First Page

56

Last Page

61

References

1. N.N.Ganixodjaev, U.A.Rozikov. Opisanie periodisheskix kraynx gibbsovskix mer nekotorx reshetoshnx modeley na dereve Keli. TMF, 1997, T.111, N1, s.109- 117. 2. Ya.G.Sinay. Teoriya fazovx perexodov. Strogie rezultat. Nauka.M.1980. 3. X.-O.Georgi. Gibbsovskie mer i fazove perexod. Moskva. "Mir" 1992. 4. R. Khakimov. New periodic Gibbs measures for q-state Potts model on a Cayley tree. Journal of Siberian Federal University, 2014, 7(3), p.297-304. 5. C. Külske, U.A.Rozikov, R.M.Khakimov. Description of all translation-invariant (splitting) Gibbs measures for the Potts model on a Cayley tree. Journal of Statistical Physics. 2014, V.156, No.1, p.189-200.

Erratum

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