U. A. Rozikov, R. M. Khakimov, F. Kh. Khaidarov, “Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree”, TMF, 196:1 (2018), 117–134; Theoret. and Math. Phys., 196:1 (2018), 1043

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Teoreticheskaya i Matematicheskaya Fizika, 2018, Volume 196, Number 1, Pages 117–134
DOI: https://doi.org/10.4213/tmf9448 (Mi tmf9448)

This article is cited in 12 scientific papers (total in 12 papers)

Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree

U. A. Rozikov^a, R. M. Khakimov^b, F. Kh. Khaidarov^c

^a Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan
^b Namangam State University, Namangan, Uzbekistan
^c Mirzo Ulugbek National University of Uzbekistan, Tashkent, Uzbekistan

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DOI: https://doi.org/10.4213/tmf9448

Abstract: We study translation-invariant Gibbs measures for the ferromagnetic Potts model with

q

$q$ states on the Cayley tree of order

k

$k$ and generalize some earlier results. We consider the question of the extremality of the known translation-invariant Gibbs measures for the Potts model with three states on the Cayley tree of order

k = 3

$k=3$ .

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

Received: 17.08.2017
Revised: 11.10.2017

English version:
Theoretical and Mathematical Physics, 2018, Volume 196, Issue 1, Pages 1043–1058
DOI: https://doi.org/10.1134/S0040577918070103

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: U. A. Rozikov, R. M. Khakimov, F. Kh. Khaidarov, “Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree”, TMF, 196:1 (2018), 117–134; Theoret. and Math. Phys., 196:1 (2018), 1043–1058

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf9448

https://doi.org/10.4213/tmf9448

https://www.mathnet.ru/eng/tmf/v196/i1/p117

This publication is cited in the following 12 articles:

Hasan Akin, Farrukh Mukhamedov, “The extremality of disordered phases for the mixed spin-(1,1/2) Ising model on a Cayley tree of arbitrary order”, J. Stat. Mech., 2024:1 (2024), 013207
Hasan Ak{\i}n, “New disordered phases of the (s,1/2)-mixed spin Ising model for arbitrary spin s”, Chaos, Solitons & Fractals, 189 (2024), 115733
M. T. Makhammadaliev, “Pure phases of the ferromagnetic Potts model with $q$ states on the Cayley tree of order three”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:4 (2024), 499–517
G. Botirov, F. Haydarov, U. Qayumov, “Gibbs measures of the Blume–Emery–Griffiths model on the Cayley tree”, Math. Phys. Anal. Geom., 26:1 (2023), 7
H. Akin, “The classification of disordered phases of mixed spin (2,1/2) Ising model and the chaoticity of the corresponding dynamical system”, Chaos, Solitons & Fractals, 167 (2023), 113086
U. A. Rozikov, M. M. Rahmatullaev, R. M. Khakimov, “Periodic Gibbs measures for the Potts model in translation-invariant and periodic external fields on the Cayley tree”, Theoret. and Math. Phys., 210:1 (2022), 135–153
F. Mukhamedov, “Extremality of disordered phase of lambda-model on Cayley trees”, Algorithms, 15:1 (2022), 18
F. M. Mukhamedov, M. M. Rahmatullaev, M. A. Rasulova, “Extremality of translation-invariant Gibbs measures for the $\lambda$ -model on the binary Cayley tree”, Theoret. and Math. Phys., 210:3 (2022), 411–424
H. Akin, F. Mukhamedov, “Phase transition for the Ising model with mixed spins on a Cayley tree”, J. Stat. Mech., 2022:5 (2022), 053204
U. A. Rozikov, “Gibbs measures of Potts model on Cayley trees: a survey and applications”, Rev. Math. Phys., 33:10 (2021), 2130007
N. M. Khatamov, “Krainost translyatsionno-invariantnykh mer Gibbsa dlya modeli Blyuma–Kapelya v sluchae “zhezl” na dereve Keli”, Ukr. Mat. Zhurn., 72:4 (2020), 540
N. M. Khatamov, “Translation-invariant extreme Gibbs measures for the Blume-Capel model withwand on a Cayley tree”, Ukr. Math. J., 72:4 (2020), 623–641

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

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