najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2016-7-5-893-899najo-1005Research ArticleСтатьиTranslation-invariant Gibbs measures for a model with logarithmic potential on a Cayley treeEshkabilovYu. Kh.

Tashkent

yusup62@mail.ruBobonazarovSh. P.

Tashkent

bshp@mail.ruTeshaboevR. I.

Termez

teshaboyev_1990@mail.ruNational University of UzbekistanUzbekistanTashkent Institute of Irrigation and MeliorationUzbekistanTermez State UniversityUzbekistan20161508202575893899Copyright © Eshkabilov Y.K., Bobonazarov S.P., Teshaboev R.I., 20252025Eshkabilov Y.K., Bobonazarov S.P., Teshaboev R.I.Eshkabilov Y.K., Bobonazarov S.P., Teshaboev R.I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1005

In this paper, we consider a model with logarithmical potential and with the set [0, 1] of spin values, on a Cayley tree Гk of the order k. In the case k = 2, 3, we shall prove that, there is a unique translation-invariant splitting Gibbs measure for this model. For the case k = 4, we show that there are three translation-invariant Gibbs measures for this model.

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The authors declare that there are no conflicts of interest present.