117

 

Biz uchinchi tartibli Keli daraxtida nol bo’lmagan tashqi maydonli SOS
modelini ko’ramiz. Bu maqolada translyatsion-invariant tashqi maydonli SOS modeli uchun
translyatsion-invariant asosiy holatlar tasniflangan.
 

  • Web Address
  • DOI
  • Date of creation in the UzSCI system 04-11-2021
  • Read count 117
  • Date of publication 15-01-2020
  • Main LanguageO'zbek
  • Pages52-58
Ўзбек

 

Biz uchinchi tartibli Keli daraxtida nol bo’lmagan tashqi maydonli SOS
modelini ko’ramiz. Bu maqolada translyatsion-invariant tashqi maydonli SOS modeli uchun
translyatsion-invariant asosiy holatlar tasniflangan.
 

Русский

 

Мы рассмотрим модели SOS с внешним полем не равным нулю на
дереве Кэли третьего порядка. В данной статье дана характеристика трансляционно-
инвариантные основные состояние модели SOS с трансляционно-инвариантным внешним
полем.
 

English

 

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

№ Author name position Name of organisation
1 Raxmatullayev M.M. Fizika-matematika fanlari doktori, Professor Namangan state university
2 Abdusalomova M.R. fizika-matematika fakulteti 5A130101-matematika yo’nalishi MM-24-18-guruh talabasi. Namangan state university
№ Name of reference
1 U.A.Rozikov “Gibbs measures on Cayley trees”. World scientific.2013.N. N. Ganikhodzhaev “Group representation and automorphi
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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