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Scientific Bulletin of Namangan State University

Abstract

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

First Page

67

Last Page

73

References

1. Georgi X.-O. Gibbsovskie mer i fazove perexod. - M.: Mir, 1992. 2. Preston K. Gibbsovskie sostoyaniya na schetnx mnojestvax. - M. : Mir, 1977. 3. Sinay Ya. G. Teoriya fazovx perexodov. Strogie rezultat. - 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 mer Gibbsa dlya modeli jestkoy serdtsevin. Teor. i matem. fizika,– 2012. – Tom 173, № 1. –C. 60-70. 7. M.Maxammadaliyev, I.O`ktamaliyev, B.Tojiboyev. HC modeli uchun davri to`rtga teng kuchsiz davriy Gibbs o’lchovlarining mavjudligi. NamDU Ilmiy axborotnomasi. 2018 y. 5-son, 13-22 betlar.

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