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Scientific Bulletin of Namangan State University

Abstract

In this article Blume-Capel model on the Cayley tree was considered. Like wise, the system of the functional equations which corresponds to for the Blume-Capel model and were the necessary and enough condition that statisfies compatibility for the Gibbs measure was found.

First Page

17

Last Page

20

References

1. Georgi X.-O. Gibbsovskie meri i fazovie perexodi. Moskva. "Mir" 1992. s. 624. 2. Preston C.J. Gibbs States on Countable Sets. - Cambridge Tracts Math., 68, Cambridge Univ. Press, Cambridge, 1974. 3. Sinay YA. G. Teoriya fazovix perexodov. Strogie rezultati.- M.: Nauka, 1980. 4. U.A. Rozikov. Gibbs measures on Cayley trees. World Scientific.-2013. 5. C.Kuiske, U.A.Rozikov, R.M.Khakimov. Deskripthion of all translation-invariant (splitting) Gibbs measures for the Potts model on a Cayley tree. Jour. Stat. Phys. 156(1) (2014), 189-200. 6. N.M.Xatamov. Novie klassi osnovnix sostoyaniy dlya modeli Pottsa s rasseyannimi konkuriruyuщimi vzaimodeystviyami na dereve Keli. TMF, 2014, T.180, №3, -s.318-328. 7. N.M.Xatamov. Ne edinstvennost meri Gibbsa dlya sharovoy modeli Izingga s radiusom vzaimodeystviya dva. TMF, 2014, T.180, №3, -s.318-328. 8. N.Xatamov, R.Xakimov. Translation-invariant Gibbs measures for the Blume-Kapel model on a Cayley tree. JMAG. 2019, Vol.15, No. 2, pp.239-255. 9. E.N.Cirillo, E.Olivieri. Metastabilty and nucleation for the Blume-Capel. Different mechanisms of transition. HEP-TH-9505055. 10. P.E.Theodorakis, N.J.Fytas. Monte Carlo study of the triangular Blume-Capel model under bond rundomness. Physical reviewe 86, 011140(2012).

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