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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 160, Number 3, Pages 507–516
DOI: https://doi.org/10.4213/tmf6412 (Mi tmf6412) 		 
This article is cited in 45 scientific papers (total in 45 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
Full-text PDF (413 kB) Citations (45)
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DOI: https://doi.org/10.4213/tmf6412
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
English version:
Theoretical and Mathematical Physics, 2009, Volume 160, Issue 3, Pages 1292–1300
DOI: https://doi.org/10.1007/s11232-009-0116-1
Bibliographic databases:
Language: Russian
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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v160/i3/p507
    • This publication is cited in the following 45 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:107
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