This article is cited in 46 papers

Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree

U. A. Rozikov^a, M. M. Rakhmatullaev<sup>b

a</sup> Institute for Mathematics and Information Technologies, Academy of Sciences of the Republic of Uzbekistan, Tashkent, Uzbekistan
^b Namangan State University, Namangan, Uzbekistan

Abstract: We introduce the notion of a weakly periodic configuration. For the Ising model with competing interactions, we describe the set of all weakly periodic ground states corresponding to normal divisors of indices $2$ and $4$ of the group representation of the Cayley tree. In addition, we study new Gibbs measures for the Ising model.

Keywords: Cayley tree, Gibbs measure, Ising model, weakly periodic ground state.

Received: 06.08.2008

DOI: 10.4213/tmf6412

 English version: Theoretical and Mathematical Physics, 2009, 160:3, 1292–1300

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