|
This article is cited in 2 scientific papers (total in 2 papers)
Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree
R. M. Khakimova, F. Kh. Khaidarovb
a Institute of Mathematics, National University of Uzbekistan named by after Mirzo Ulugbek, Tashkent, Uzbekistan
b Mirzo Ulugbek National University of Uzbekistan, Tashkent,
Uzbekistan
Abstract:
We study translation-invariant Gibbs measures on a Cayley tree of order $k=3$ for the ferromagnetic three-state Potts model. We obtain explicit formulas for translation-invariant Gibbs measures. We also consider periodic Gibbs measures on a Cayley tree of order $k$ for the antiferromagnetic $q$-state Potts model. Moreover, we improve previously obtained results: we find the exact number of periodic Gibbs measures with the period two on a Cayley tree of order $k\ge3$ that are defined on some invariant sets.
Keywords:
Cayley tree, configuration, Potts model, Gibbs measure, translation-invariant measure, periodic measure
DOI:
https://doi.org/10.4213/tmf9138
 Full text:
PDF file (434 kB)
References:
PDF file
HTML file
English version:
Theoretical and Mathematical Physics, 2016, 189:2, 1651–1659
Bibliographic databases:
    
Received: 22.12.2015
Citation:
R. M. Khakimov, F. Kh. Khaidarov, “Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree”, TMF, 189:2 (2016), 286–295; Theoret. and Math. Phys., 189:2 (2016), 1651–1659
Citation in format AMSBIB
\Bibitem{KhaKha16}
\by R.~M.~Khakimov, F.~Kh.~Khaidarov
\paper Translation-invariant and periodic Gibbs measures for the~Potts model on a~Cayley tree
\jour TMF
\yr 2016
\vol 189
\issue 2
\pages 286--295
\mathnet{http://mi.mathnet.ru/tmf9138}
\crossref{https://doi.org/10.4213/tmf9138}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3589035}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2016TMP...189.1651K}
\elib{https://elibrary.ru/item.asp?id=27485058}
\transl
\jour Theoret. and Math. Phys.
\yr 2016
\vol 189
\issue 2
\pages 1651--1659
\crossref{https://doi.org/10.1134/S004057791611009X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000389995500009}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85002644042}
Linking options:
http://mi.mathnet.ru/eng/tmf9138https://doi.org/10.4213/tmf9138 http://mi.mathnet.ru/eng/tmf/v189/i2/p286
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:
-
U. A. Rozikov, R. M. Khakimov, F. Kh. Khaidarov, “Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 196:1 (2018), 1043–1058
 -
R. M. Khakimov, M. T. Makhammadaliev, “Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 199:2 (2019), 726–735
|
| Number of views: |
| This page: | 189 | | Full text: | 31 | | References: | 25 | | First page: | 13 |
|
Terms of Use