Article

Translation-invariant Gibbs measures for a model with logarithmic potential on a Cayley tree

Yu. Kh. ÈshkabilovNational University of Uzbekistan, Tashkent, UzbekistanSh.P. BobonazarovTashkent Institute of Irrigation and Melioration, Tashkent, UzbekistanR.I. TeshaboevTermez State University, Termez, Uzbekistan

Nanosystems Physics Chemistry Mathematicsjournal2016en

ABI

Abstract

In this paper, we consider a model with logarithmical potential and with the set [0, 1] of spin values, on a Cayley tree k 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.

Topics

Theoretical and Computational Physics Quantum chaos and dynamical systems Opinion Dynamics and Social Influence

Identifiers

DOI: 10.17586/2220-8054-2016-7-5-893-899

Citations and references

Cited by 1 13 references

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