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Scientific Bulletin of Namangan State University

Abstract

We consider the SOS model with non-zero external field on the Cayley tree of order 3 k  . Described translation-invariant ground states for the model of SOS with translation-invariant external field.

First Page

52

Last Page

57

References

1. U.A.Rozikov “Gibbs measures on Cayley trees”. World scientific.2013. 2. N. N. Ganikhodzhaev “Group representation and automorphisms of the Cayley tree”, Dokl. Akad. nauk Resp. Uzbekistan, no. 4, 3 (1994) [in Russian]. 3. F.Mukhamedov, Ch.Hee Pah, M.Rahmatullaev, H.Jamil. “Periodic and Weakly Periodic Ground States for the λ− Model on Cayley Tree”. 2017.Journal of Physics: Conf. Series 949, 012021, doi:10.1088/1742−6596/949/1/012021. 4. M. I. Kargapolov, Yu. I. Merzlyakov “Fundamentals of the Theory of Groups” (Springer-Verlag, New York-Heidelberg-Berlin, 1979). [Fundamentals of Group Theory(Nauka, Moscow, 1982)]. 5. U.A.Rozikov “ A contructite Description of Grond States and Gibbs Measures for Ising Model with two step interations on Cayley tree”. 2006. Journal of statistical Physics. Vol. 122. N2. 6. M. M. Rahmatullaev “ Description of Weak Periodic Ground States of Ising Model with Competing Interactions on Cayley Tree”. 2010.Applied Mathematics & Information Sciences 4(2), 237251. 7. M.M.Rakhmatullaev, M.A.Rasulova “Periodic and Weakly Periodic Ground States for the Potts Model with Competing Interactions on the Cayley Tree”. 2016. ISSN 1055 − 1344, Siberian Advances in Mathematics, Vol. 26, No.3, pp.215229. 8. U. A.Rozikov, M. M. Rahmatullaev “Weakly Periodic Ground States and Gibbs Measures for the Ising Model with Competing Interactions on the Cayley Tree”, Theor. Math. Phys. 160, No. 3, 1292–1300 (2009). 9. M.M.Rahmatullaev, M.A.Rasulova “Ground States for the Ising model with an external field on the Cayley tree”, Uz. Math. Journal, No. 3, 147–155 (2018). 10. M. M.Rahmatullaev, M.R.Abdusalomova, M.A.Rasulova “Ground states for the SOS model with an external field on the Cayley tree” Phys.Math.Journal Arxiv.[1908.02457].

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