This article is cited in 16 papers

Periodic and weakly periodic ground states for the Potts model with competing interactions on the Cayley tree

M. A. Rasulova^a, M. M. Rahmatullaev<sup>b

a</sup> Namangan State University, Namangan, Uzbekistan
^b National University of Uzbekistan, Institute of Mathematics, Tashkent, Uzbekistan

Abstract: We consider the Potts model with competing interactions on the Cayley tree of order $k$ with $k\geq 2$. We describe the sets of periodic and weakly periodic ground states corresponding to normal subgroups of the group representation of the Cayley tree of index $4$.

Key words: Cayley tree, Potts model, periodic and weakly periodic ground states.

UDC: 517.98+530.1

Received: 09.07.2014

DOI: 10.17377/mattrudy.2015.18.207

 English version: Siberian Advances in Mathematics, 2016, 26:3, 215–229

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