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This article is cited in 44 scientific papers (total in 44 papers)
Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree
U. A. Rozikova, M. M. Rakhmatullaevb a 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
Citation:
U. A. Rozikov, M. M. Rakhmatullaev, “Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree”, TMF, 160:3 (2009), 507–516; Theoret. and Math. Phys., 160:3 (2009), 1292–1300
Linking options:
https://www.mathnet.ru/eng/tmf6412https://doi.org/10.4213/tmf6412 https://www.mathnet.ru/eng/tmf/v160/i3/p507
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Abstract page: | 580 | Full-text PDF : | 235 | References: | 104 | First page: | 4 |
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