Rustamjon M. Khakimov, “New periodic Gibbs measures for $q$-state Potts model on a Cayley tree”, J. Sib. Fed. Univ. Math. Phys., 7:3 (2014), 297

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Journal of Siberian Federal University. Mathematics & Physics, 2014, Volume 7, Issue 3, Pages 297–304 (Mi jsfu374)

This article is cited in 6 scientific papers (total in 6 papers)

New periodic Gibbs measures for

q

$q$ -state Potts model on a Cayley tree

Rustamjon M. Khakimov

Institute of Mathematics, National University of Uzbekistan, Do’rmon Yo’li, 29, Tashkent, 100125, Uzbekistan

Full-text PDF (162 kB) Citations (6)

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Abstract: In this paper under some conditions on parameters of the

q

$q$ -state Potts model on a Cayley tree of order k we prove existence of the periodic (non translation-invariant) Gibbs measures. Also we give a result about the number of such measures.

Keywords: Cayley tree, configuration, Potts model, Gibbs measure, periodic Gibbs measures, translation-invariant measures.

Received: 06.03.2014
Received in revised form: 29.04.2014
Accepted: 26.05.2014

Document Type: Article

UDC: 517.98

Language: English

Citation: Rustamjon M. Khakimov, “New periodic Gibbs measures for

q

$q$ -state Potts model on a Cayley tree”, J. Sib. Fed. Univ. Math. Phys., 7:3 (2014), 297–304

Citation in format AMSBIB

\Bibitem{Kha14}

\by Rustamjon~M.~Khakimov

\paper New periodic Gibbs measures for $q$-state Potts model on a Cayley tree

\jour J. Sib. Fed. Univ. Math. Phys.

\yr 2014

\vol 7

\issue 3

\pages 297--304

\mathnet{http://mi.mathnet.ru/jsfu374}

Linking options:

https://www.mathnet.ru/eng/jsfu374

https://www.mathnet.ru/eng/jsfu/v7/i3/p297

This publication is cited in the following 6 articles:

M. M. Rahmatullaev, Zh. D. Dekhkonov, “Potts model on a Cayley tree: a new class of Gibbs measures”, Theoret. and Math. Phys., 215:1 (2023), 586–597
Rozikov U.A., “Gibbs Measures of Potts Model on Cayley Trees: a Survey and Applications”, Rev. Math. Phys., 33:10 (2021), 2130007
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
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, F. Kh. Khaidarov, “Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree”, Theoret. and Math. Phys., 189:2 (2016), 1651–1659
F. Haydarov, R. Khakimov, “An improvement of extremality regions for Gibbs measures of the Potts model on a Cayley tree”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, eds. S. Ayupov, V. Chilin, N. Ganikhodjaev, F. Mukhamedov, I. Rakhimov, IOP Publishing Ltd, 2016, 012019

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

Журнал Сибирского федерального университета. Серия "Математика и физика"

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References:	63

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