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Scientific Bulletin of Namangan State University

Abstract

We study one of fertile Hard-Core (HC) models with four states on Cayley tree of order six and seven. In the case of the fertile ‚Stick‛ graph, the exact values of the parameters are found for which the translation-invariant Gibbs measure is not unique.

First Page

35

Last Page

41

References

1.‖‖Georgi‖X.-O.‖Gibbsovskiye‖meri‖i‖fazovie‖perexodi. - M.:‖Mir,‖1992. 2.‖‖Sinay‖Ya.‖G.‖Teoriya‖fazovix‖perexodov.‖Strogiye rezultati. - M.: Nauka, 1980. 3. Rozikov U. A. Gibbs measures on Cayley trees. Singapore: World Sci., 2013. 4. Khakimov R.M. The uniqueness of the Translation-invariant Gibbs measure for four state HC-models on a Cayley tree. Journal of Siberian Federal University. Mathematics and Physics. – 2015, 8(2), –P.165-172. 5.‖Xakimov‖R.M.‖Meri‖Gibbsa‖dlya‖plodorodnix‖modeley‖jestkoy‖serdchevini‖na‖dereve‖ Keli. Teor. i matem. fizika,– 2016. – Tom 186,‖№‖2.‖–C.‖ 340-352. 6. Brightwell G., Winkler P. Graph homomorphisms and phase transitions. J. Combin. Theor, Series B. – 1999. – V. 77. – P. 221- 262.

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