M. M. Rahmatullaev, O. N. Khakimov, A. M. Tukhtaboev, “A $p$-adic generalized Gibbs measure for the Ising model on a Cayley tree”, TMF, 201:1 (2019), 126–136; Theoret. and Math. Phys., 201:1 (2019), 1521

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Teoreticheskaya i Matematicheskaya Fizika, 2019, Volume 201, Number 1, Pages 126–136
DOI: https://doi.org/10.4213/tmf9711 (Mi tmf9711)

This article is cited in 10 scientific papers (total in 10 papers)

A

$p$ -adic generalized Gibbs measure for the Ising model on a Cayley tree

M. M. Rahmatullaev^ab, O. N. Khakimov^b, A. M. Tukhtaboev^c

^a Namangam State University, Namangan, Uzbekistan
^b Institute of Mathematics, National University of Uzbekistan named by after Mirzo Ulugbek, Tashkent, Uzbekistan
^c Namangan Construction Institute, Namangan, Uzbekistan

Full-text PDF (481 kB) Citations (10)

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DOI: https://doi.org/10.4213/tmf9711

Abstract: We consider a

$p$ -adic Ising model on the Cayley tree of order

$k\ge2$ . We completely describe all

$p$ -adic translation-invariant generalized Gibbs measures for

$k=3$ . Moreover, we show the existence of a phase transition for the

$p$ -adic Ising model for any

$k\ge3$ if

$p\equiv1\!\pmod4$ .

Keywords:

$p$ -adic number, Ising model, Gibbs measure, phase transition.

Received: 25.02.2019
Revised: 01.04.2019

English version:
Theoretical and Mathematical Physics, 2019, Volume 201, Issue 1, Pages 1521–1530
DOI: https://doi.org/10.1134/S004057791910009X

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: M. M. Rahmatullaev, O. N. Khakimov, A. M. Tukhtaboev, “A

$p$ -adic generalized Gibbs measure for the Ising model on a Cayley tree”, TMF, 201:1 (2019), 126–136; Theoret. and Math. Phys., 201:1 (2019), 1521–1530

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf9711

https://doi.org/10.4213/tmf9711

https://www.mathnet.ru/eng/tmf/v201/i1/p126

This publication is cited in the following 10 articles:

Muzaffar M. Rahmatullaev, Zulxumor T. Abdukaxorova, “On H-Weakly Periodic P-Adic Generalized Gibbs Measures of P-Adic Ising Model with an External Field on a Cayley Tree”, Reports on Mathematical Physics, 95:1 (2025), 93
M. M. Rahmatullaev, Z. T. Abdukaxorova, “ $\boldsymbol{H}_{\boldsymbol{A}}$ -Weakly Periodic $\boldsymbol{p}$ -Adic Generalized Gibbs Measures for Ising Model on a Cayley Tree”, Lobachevskii J Math, 45:1 (2024), 504
Muzaffar Rahmatullaev, Zulxumor Abdukaxorova, “ $H_A$ -Weakly Periodic $p$ -Adic Generalized Gibbs Measures for the $p$ -Adic Ising Model on the Cayley Tree of Order Two”, P-Adic Num Ultrametr Anal Appl, 16:3 (2024), 233
Muzaffar Rahmatullaev, Akbarkhuja Tukhtabaev, Nurkhon Samijonova, “Weakly periodic p-adic quasi-Gibbs measures for the Potts model on a Cayley tree”, Lett Math Phys, 114:6 (2024)
F. M. Mukhamedov, M. M. Rahmatullaev, A. M. Tukhtabaev, R. Mamadjonov, “The $p$ -adic Ising model in an external field on a Cayley tree: periodic Gibbs measures”, Theoret. and Math. Phys., 216:2 (2023), 1238–1253
M. Rahmatullaev, A. Tukhtabaev, “Some non-periodic $p$ -adic generalized Gibbs measures for the Ising model on a Cayley tree of order $k$ ”, Math. Phys. Anal. Geom., 26:3 (2023), 22
M. Rahmatullaev, A. Tukhtabaev, “On periodic $p$ -adic generalized Gibbs measures for Ising model on a Cayley tree”, Lett. Math. Phys., 112:6 (2022)
Mukhamedov F., Khakimov O., “Translation-Invariant Generalized P-Adic Gibbs Measures For the Ising Model on Cayley Trees”, Math. Meth. Appl. Sci., 44:16 (2021), 12302–12316
A. Tukhtabaev, “On g(2)-periodic quasi Gibbs measures of p-adic Potts model on a Cayley tree”, P-Adic Numbers Ultrametric Anal. Appl., 13:4 (2021), 291–307
Farrukh Mukhamedov, Otabek Khakimov, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, Advances in Non-Archimedean Analysis and Applications, 2021, 115

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

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