M. M. Rakhmatullaev, “Weakly periodic Gibbs measures and ground states for the Potts model with competing interactions on the Cayley tree”, TMF, 176:3 (2013), 477–493; Theoret. and Math. Phys., 176:3 (2013), 1236

Teoreticheskaya i Matematicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Guidelines for authors
	License agreement
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

TMF:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 176, Number 3, Pages 477–493
DOI: https://doi.org/10.4213/tmf8530 (Mi tmf8530)

This article is cited in 26 scientific papers (total in 26 papers)

Weakly periodic Gibbs measures and ground states for the Potts model with competing interactions on the Cayley tree

M. M. Rakhmatullaev

Namangant State University, Uzbekistan

Full-text PDF (424 kB) Citations (26)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf8530

Abstract: For the Potts model with competing interactions, we describe the set of weakly periodic ground states corresponding to index-two normal divisors of the Cayley tree group representation. We also study some weakly periodic Gibbs measures.

Keywords: Cayley tree, Gibbs measure, Potts model, weakly periodic ground state.

Received: 11.03.2013

English version:
Theoretical and Mathematical Physics, 2013, Volume 176, Issue 3, Pages 1236–1251
DOI: https://doi.org/10.1007/s11232-013-0103-4

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: M. M. Rakhmatullaev, “Weakly periodic Gibbs measures and ground states for the Potts model with competing interactions on the Cayley tree”, TMF, 176:3 (2013), 477–493; Theoret. and Math. Phys., 176:3 (2013), 1236–1251

Citation in format AMSBIB

\Bibitem{Rah13}

\by M.~M.~Rakhmatullaev

\paper Weakly periodic Gibbs measures and ground states for the~Potts model with competing interactions on the~Cayley tree

\jour TMF

\yr 2013

\vol 176

\issue 3

\pages 477--493

\mathnet{http://mi.mathnet.ru/tmf8530}

\crossref{https://doi.org/10.4213/tmf8530}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3230746}

\zmath{https://zbmath.org/?q=an:1286.82005}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2013TMP...176.1236R}

\elib{https://elibrary.ru/item.asp?id=20732663}

\transl

\jour Theoret. and Math. Phys.

\yr 2013

\vol 176

\issue 3

\pages 1236--1251

\crossref{https://doi.org/10.1007/s11232-013-0103-4}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000325707900011}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84885643304}

Linking options:

https://www.mathnet.ru/eng/tmf8530

https://doi.org/10.4213/tmf8530

https://www.mathnet.ru/eng/tmf/v176/i3/p477

This publication is cited in the following 26 articles:

M. M. Rahmatullaev, B. M. Isakov, “Translation-invariant Gibbs measures for the Ising–Potts model on a second-order Cayley tree”, Theoret. and Math. Phys., 219:3 (2024), 1048–1059
Begzod Isakov, Olimkhon Akhmedov, “FUNKTsIONALNYE URAVNENIYa DLYa PREDELNYKh MER GIBBSA MODELI IZINGA-POTTSA NA DEREVE KELI”, VOGUMFT, 2024, no. 1(4), 90
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
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
M. M. Rahmatullaev, B. M. Isakov, “Ground states of Ising-Potts model on Cayley tree”, Ufa Math. J., 15:1 (2023), 43–55
M. M. Rakhmatullaev, M. A. Rasulova, “Opisanie slabo periodicheskikh osnovnykh sostoyanii dlya modeli Pottsa s vneshnim polem i schetnym mnozhestvom znachenii spina na dereve Keli”, Vladikavk. matem. zhurn., 25:4 (2023), 103–119
Dilshod O. Egamov, “Periodic and weakly periodic ground states corresponding to the subgroups of index three for the Ising model on the Cayley tree of order three”, Ukr. Mat. Zhurn., 75:6 (2023), 793
Dilshod O. Egamov, “Periodic and Weakly Periodic Ground States Corresponding to the Subgroups of Index Three for the Ising Model on the Cayley Tree of Order Three”, Ukr Math J, 75:6 (2023), 908
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
Muzaffar M. Rahmatullaev, Bunyod U. Abraev, “On ground states for the SOS model with competing interactions”, Zhurn. SFU. Ser. Matem. i fiz., 15:2 (2022), 162–175
M. M. Rahmatullaev, M. A. Rasulova, “Periodic Ground States for the Potts Model with External Field and a Countable Set of Spin Values on the Cayley Tree”, Math. Notes, 112:1 (2022), 116–125
J. D. Dekhkonov, “On $(k_0)$-translation-invariant and $(k_0)$-periodic Gibbs measures for Potts model on Cayley tree”, Ufa Math. J., 14:4 (2022), 42–55
G. I. Botirov, U. U. Qayumov, “Ground states for the Potts model with competing interactions and a countable set of spin values on a Cayley tree”, Theoret. and Math. Phys., 209:2 (2021), 1633–1642
Rahmatullaev M.M. Egamov D.O. Haydarov F.H., “Periodic and Weakly Periodic Ground States Corresponding to Subgroups of Index Three For the Ising Model on Cayley Tree”, Rep. Math. Phys., 88:2 (2021), 247–257
Rahmatullaev M.M. Rafikov F.K. Azamov Sh.Kh., “On the Constructive Description of Gibbs Measures For the Potts Model on a Cayley Tree”, Ukr. Math. J., 73:7 (2021), 1092–1106
M. Rahmatullaev, F. K. Rafikov, Sh. Kh. Azamov, “Pro konstruktivnі opisi mіr Gіbbsa dlya modelі Pottsa na derevі Kelі”, Ukr. Mat. Zhurn., 73:7 (2021), 938
Mukhamedov F.M., Rakhmatullaev M.M., Rasulova M.A., “Weakly Periodic Ground States For the Lambda-Model”, Ukr. Math. J., 72:5 (2020), 771–784
Farrukh M. Mukhamedov, Muzaffar M. Rahmatullaev, M. A. Rasulova, “Slabo periodicheskie osnovnye sostoyaniya dlya λ-modeli”, Ukr. Mat. Zhurn., 72:5 (2020)
F. Mukhamedov, Ch. H. Pah, M. Rahimatullaev, H. Jamil, “Periodic and weakly periodic ground states for the $\lambda$-model on Cayley tree”, 4th International Conference on Mathematical Applications in Engineering 2017 (ICMAE'17), Journal of Physics Conference Series, 949, ed. A. Rakhimov, B. Ural, J. Daoud, K. Saburov, M. Chowdhury, IOP Publishing Ltd, 2018, UNSP 012021
G. I. Botirov, M. M. Rahmatullaev, Springer Proceedings in Mathematics & Statistics, 264, Algebra, Complex Analysis, and Pluripotential Theory, 2018, 59

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

Statistics & downloads:
Abstract page:	462
Full-text PDF :	178
References:	53
First page:	7

Что такое QR-код?

Registration to the website

Logotypes