This article is cited in 25 papers

Potts model with competing interactions on the Cayley tree: The contour method

G. I. Botirov^a, U. A. Rozikov<sup>b

a</sup> National University of Uzbekistan named after M. Ulugbek
^b Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We consider the Potts model with three spin values and with competing interactions of radius $r=2$ on the Cayley tree of order $k=2$. We completely describe the ground states of this model and use the contour method on the tree to prove that this model has three Gibbs measures at sufficiently low temperatures.

Keywords: Cayley tree, configuration, contour method, ground state, Gibbs measure.

Received: 11.12.2006

DOI: 10.4213/tmf6123

 English version: Theoretical and Mathematical Physics, 2007, 153:1, 1423–1433

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