On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree

In the paper, we study the q-state (where q = 3, 4, 5, ... ) Potts model with special external field on a Cayley tree of order k ≥ 2. For antiferromagnetic Potts model with such an external field on the Cayley tree of order k ≥ 6, the non-uniqueness of weakly periodic (non-periodic) Gibbs measures i...

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Bibliographic Details
Date:2016
Main Author: Rahmatullaev, M.M.
Format: Article
Language:English
Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2016
Series:Журнал математической физики, анализа, геометрии
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/140557
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:On Weakly Periodic Gibbs Measures of the Potts Model with a Special External Field on a Cayley Tree / M.M. Rahmatullaev // Журнал математической физики, анализа, геометрии. — 2016. — Т. 12, № 4. — С. 302-314. — Бібліогр.: 16 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:In the paper, we study the q-state (where q = 3, 4, 5, ... ) Potts model with special external field on a Cayley tree of order k ≥ 2. For antiferromagnetic Potts model with such an external field on the Cayley tree of order k ≥ 6, the non-uniqueness of weakly periodic (non-periodic) Gibbs measures is proved. The weakly periodic Gibbs measures for the Potts model with zero external field are also studied. It is proved that under some conditions imposed on the parameters of the model there can be not less than 2q - 2 such measures.