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Sibirsk. Mat. Zh., 2015, Volume 56, Number 5, Pages 1163–1170 (Mi smj2705)  

A weakly periodic Gibbs measure for the ferromagnetic Potts model on a Cayley tree

M. M. Rahmatullaev

Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan

Abstract: We study the Potts model with $q$ states in a Cayley tree of order $k\ge2$. For the ferromagnetic Potts model, we prove the existence of a weakly periodic Gibbs measure that is not translation-invariant.

Keywords: Cayley tree, Gibbs measure, Potts model, weakly periodic Gibbs measure.

DOI: https://doi.org/10.17377/smzh.2015.56.515

Full text: PDF file (290 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:5, 929–935

Bibliographic databases:

UDC: 517.98+530.1
Received: 17.11.2014

Citation: M. M. Rahmatullaev, “A weakly periodic Gibbs measure for the ferromagnetic Potts model on a Cayley tree”, Sibirsk. Mat. Zh., 56:5 (2015), 1163–1170; Siberian Math. J., 56:5 (2015), 929–935

Citation in format AMSBIB
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\by M.~M.~Rahmatullaev
\paper A weakly periodic Gibbs measure for the ferromagnetic Potts model on a~Cayley tree
\jour Sibirsk. Mat. Zh.
\yr 2015
\vol 56
\issue 5
\pages 1163--1170
\mathnet{http://mi.mathnet.ru/smj2705}
\crossref{https://doi.org/10.17377/smzh.2015.56.515}
\elib{http://elibrary.ru/item.asp?id=24817504}
\transl
\jour Siberian Math. J.
\yr 2015
\vol 56
\issue 5
\pages 929--935
\crossref{https://doi.org/10.1134/S0037446615050158}
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