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Scientific Bulletin of Namangan State University

Abstract

We study the hard-core model on the Cayley tree. For this model we find new conditions of uniqueness of weakly periodic Gibbs measures for a normal divisor of index four

First Page

3

Last Page

7

References

1. X.O. Georgi. Gibbsovskie meri i fazovie perexodi. Moskva. "Mir" 1992. 2. C. J. Preston. Gibbs States on Countable Sets, Cambridge Tracts Math., 68, Cambridge Univ. Press, Cambridge, 1974. 3. YA. G. Sinay. Teoriya fazovix perexodov. Strogie rezultati, Moskva. "Nauka " 1980. 4. U.A. Rozikov. Gibbs measures on Cayley trees. World Scientific -2013. 5. R.M. Xakimov. Slabo periodicheskie meri Gibbsa dlya NS-modeli dlya normalnogo delitelya indeksa chetire, UkrMJ, 2015, t. 67, No 10, str.1409-1422.

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