This article is cited in 17 papers

The existence of weakly periodic Gibbs measures for the Potts model on a Cayley tree

M. M. Rakhmatullaev

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

Abstract: We study the $q$-state Potts model on a Cayley tree of order $k\ge2$. In the group representation of the Cayley tree for the ferromagnetic Potts model, we single out a set of index-$2$ subgroups under which each weakly periodic Gibbs measure is translation invariant. For the anti-ferromagnetic Potts model with $k\ge2$ and $q\ge 2$, we show that a weakly periodic Gibbs measure that is not translation invariant is not unique.

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

Received: 01.02.2014

DOI: 10.4213/tmf8647

 English version: Theoretical and Mathematical Physics, 2014, 180:3, 1019–1029

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