272

 

We study weakly periodic Ground States for the model of SOS with competing
interactions on the Cayley tree of order two.
 

  • Web Address
  • DOI
  • Date of creation in the UzSCI system 20-12-2021
  • Read count 272
  • Date of publication 20-12-2021
  • Main LanguageIngliz
  • Pages14-21
English

 

We study weakly periodic Ground States for the model of SOS with competing
interactions on the Cayley tree of order two.
 

Русский

 

В работе для нормального делителя индекса два изушается слабо-
периодишеских основных состояниях для модели SOS с конкурирующими
взаимодействиями на дереве Кэли порядка два.
 

Ўзбек

 

Ushbu maqolada indeksi 2 ga teng bo’lgan normal bo’luvchiga nisbatan 2 tartibli Keli daraxtida raqobatlashuvchi o’zaro tasirli SOS modeli uchun kuchsiz davriy asosiy
holatlar o’rganiladi.
 

№ Author name position Name of organisation
1 Abraev B.O. O'qituvchi Chirchik State Pedagogical Institute
№ Name of reference
1 К.Престон,‖ Гиббсовские‖ состоѐниѐ‖ на‖сшетных‖множествах,‖ Мир,‖М.,‖1977.
2 U.A.Rozikov, 2013 Gibbs Measures on Cayley Trees, World Scientific, Hackensack.
3 R.Fernandez, Contour ensembles and the description of Gibbsian probability distributions at low temperature, http://www.univ-rouen.fr LMRS Persopage Fernandez resucont.html, 1998.
4 U.A.Rozikov‖ and‖ M.M.Rakhmatullaev,‚Weakly‖ periodic‖ ground‖ states‖ and‖ Gibbs‖ measures‖ for‖ the‖ Ising‖ model‖ with‖ competing‖ interactions‖ on‖ the‖ Cayley‖ tree,‛Theoret.‖ Math. Phys.160, 1292 (2009) [Teor. Mat. Fiz.160, 507 2009)].
5 M.M.Rakhmatullaev,‚Description of weak periodic ground states of Ising model with competing‖ interactions‖ on‖Cayley‖tree,‛Appl.‖ Math.‖Inf.‖Sci.4,‖237‖(2010).
6 ‖ M.M.Rakhmatullaev,‚Weakly‖ periodic‖ Gibbs‖ measures‖ and‖ ground‖ states‖ for‖ the‖ Potts‖ model with competing interactions on the‖ Cayley‖ tree,‛Theoret.‖ Math.‖ Phys.176,‖ 1236‖ (2013) [Teor. Mat. Fiz. 176, 477 (2013)].
7 M.M.Rahmatullaev, M.A.Rasulova., Periodic and Weakly Periodic Ground States for the Potts Model with Competing Interactions on the Cayley Tree. Siberian Advances in Mathematics, 2016, Vol. 26, No. 3, pp. 215–229.
8 U.A.Rozikov., Description of limit Gibbs measures for models on Bethe lattices. Siberian Mathematical Journal, Vol. 39, No. 2, 1998
9 O.Melnikov, R.I.Tyshkevich, V.A.Yemelichev, and V.I.Sarvanov, Lectures on Graph Theory (B.I.Wissenschaftsverlag, Mannheim, 1994) [Lectures on Graph Theory. Textbook (Nauka, Moscow, 1990)].
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