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 TMF, 2003, Volume 135, Number 3, Pages 515–523 (Mi tmf201)

Periodic Gibbs Measures for the Ising Model with Competing Interactions

Kh. A. Nazarova, U. A. Rozikovb

a Samarkand State Institute of Architecture and Construction
b Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: For the Ising model with competing interactions on the second-order Cayley tree, we find the operator corresponding to the periodic Gibbs distributions with period two and determine the invariant subsets of this operator, which are used to describe the periodic Gibbs distributions.

Keywords: Cayley tree, configuration, limit Gibbs measure, periodic Gibbs measure

DOI: https://doi.org/10.4213/tmf201

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English version:
Theoretical and Mathematical Physics, 2003, 135:3, 881–888

Bibliographic databases:

Citation: Kh. A. Nazarov, U. A. Rozikov, “Periodic Gibbs Measures for the Ising Model with Competing Interactions”, TMF, 135:3 (2003), 515–523; Theoret. and Math. Phys., 135:3 (2003), 881–888

Citation in format AMSBIB
\Bibitem{NazRoz03} \by Kh.~A.~Nazarov, U.~A.~Rozikov \paper Periodic Gibbs Measures for the Ising Model with Competing Interactions \jour TMF \yr 2003 \vol 135 \issue 3 \pages 515--523 \mathnet{http://mi.mathnet.ru/tmf201} \crossref{https://doi.org/10.4213/tmf201} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1984454} \zmath{https://zbmath.org/?q=an:1178.82019} \transl \jour Theoret. and Math. Phys. \yr 2003 \vol 135 \issue 3 \pages 881--888 \crossref{https://doi.org/10.1023/A:1024091206594} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000184367300012} 

• http://mi.mathnet.ru/eng/tmf201
• https://doi.org/10.4213/tmf201
• http://mi.mathnet.ru/eng/tmf/v135/i3/p515

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Rozikov, UA, “A constructive description of ground states and Gibbs measures for Ising model with two-step interactions on Cayley tree”, Journal of Statistical Physics, 122:2 (2006), 217
2. U. A. Rozikov, M. M. Rakhmatullaev, “Weakly periodic ground states and Gibbs measures for the Ising model with competing interactions on the Cayley tree”, Theoret. and Math. Phys., 160:3 (2009), 1292–1300
3. Rahmatullaev M.M., “Description of Weak Periodic Ground States of Ising Model with Competing Interactions on Cayley Tree”, Applied Mathematics & Information Sciences, 4:2 (2010), 237–251
4. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001
5. Akin H., “Gibbs Measures of An Ising Model With Competing Interactions on the Triangular Chandelier-Lattice”, Condens. Matter Phys., 22:2 (2019), 23002
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