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Scientific Bulletin of Namangan State University

Abstract

We study Hard-Core (HC) model on Cayley tree of order two. For a two states HC-model the exact number of periodic (not translation-invariant) Gibbs measures is found.

First Page

3

Last Page

8

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. 46 (1/2) (2004),–P. 197-212. 6.Rozikov U.A., Xakimov R.M. Uslovie edinstvennosti slabo periodicheskoy meri Gibbsa dlya modeli jestkoy serdsevini. Teor. i matem. fizika,–2012.–Tom 173, № 1. –C. 60-70.

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