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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 conditions of uniqueness of weakly periodic Gibbs measures for a normal divisor of index four.

First Page

16

Last Page

23

References

1. Georgi X.O. Gibbsovskie meri i fazovie perexodi. - M.: Mir, 1992. 2. Preston K. Gibbsovskie sostoyaniya na schetnix mnojestvax. - M. : Mir, 1977. 3. Sinay Ya. G. Teoriya fazovix perexodov. Strogie rezultati. - M.: Nauka, 1980. 4. Rozikov U. A. Gibbs measures on Cayley trees. Singapore: World Sci., 2013. 5. Suhov Yu. M., Rozikov U. A. A hard-core model on a Cayley tree: an example of a loss network. Queueing Syst.. 2004. V. 46. P. 197–212. 6. Xakimov R. M. Slabo periodicheskie meri Gibbsa dlya NS-modeli dlya normalnogo delitelya indeksa chetire. Ukr. mat. jurn.. 2015. T. 67, № 10. S. 1409–1422. 7. Khakimov R.M., Madgoziyev G.T. Weakly periodic Gibbs measures for two and three state HC models on a Cayley tree. UzMJ, 2018, -№ 3, p. 116-131.

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