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Scientific Bulletin of Namangan State University

Abstract

We study the Potts model on the Cayley tree. We improved one of the previously known results. We proved that on one of the invariant sets for the Potts model with a zero external field there exist exactly two periodic (not translation-invariant) Gibbs measures

First Page

3

Last Page

8

References

1. Georgi X.-O. Gibbsovskie meri i fazovie perexodi. Moskva. "Mir" 1992. 2. Preston C. J. Gibbs States on Countable Sets, Cambridge Tracts Math., 68, Cambridge Univ. Press, Cambridge, 1974. 3. Sinay Ya. G. Teoriya fazovix perexodov. Strogie rezultati, Nauka, M., 1980. 4. Rozikov U.A. Gibbs measures on Cayley trees. World Scientific.-2013. 5. Ganixodjaev N.N., Rozikov U.A. Opisanie periodicheskix kraynix gibbsovskix mer nekotorix modeley na dereve Keli. // TMF, 111: 1 (1997), 109–117. 6. Rozikov U.A., Xakimov R.M. Periodicheskie meri Gibbsa dlya modeli Pottsa na dereve Keli. // TMF, 175: 2 (2013), 300–312. 7. Xakimov R.M. O sushestvovanii periodicheskix mer Gibbsa dlya modeli Pottsa na dereve Keli. // Uzb. mat. jurnal. –Tashkent, 2014. -№ 3. -C. 134-142.

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