U. A. Rozikov, Sh. A. Shoyusupov, “Fertile HC models with three states on a Cayley tree”, TMF, 156:3 (2008), 412–424; Theoret. and Math. Phys., 156:3 (2008), 1319

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, 2008, Volume 156, Number 3, Pages 412–424
DOI: https://doi.org/10.4213/tmf6256 (Mi tmf6256)

This article is cited in 24 scientific papers (total in 24 papers)

Fertile HC models with three states on a Cayley tree

U. A. Rozikov^ab, Sh. A. Shoyusupov^a

^a Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan
^b GC University, Abdus Salam School of Mathematical Sciences

Full-text PDF (484 kB) Citations (24)

References:

PDF

HTML

DOI: https://doi.org/10.4213/tmf6256

Abstract: We consider fertile hard-core (HC) models with three states on a homogeneous Cayley tree. It is known that four types of such models exist. For these models, we describe the translation-invariant and periodic HC Gibbs measures. We also construct a uncountable set of nonperiodic Gibbs measures.

Keywords: Cayley tree, configuration, HC model, Gibbs measure.

Received: 10.07.2007

English version:
Theoretical and Mathematical Physics, 2008, Volume 156, Issue 3, Pages 1319–1330
DOI: https://doi.org/10.1007/s11232-008-0109-5

Bibliographic databases:

Language: Russian

Citation: U. A. Rozikov, Sh. A. Shoyusupov, “Fertile HC models with three states on a Cayley tree”, TMF, 156:3 (2008), 412–424; Theoret. and Math. Phys., 156:3 (2008), 1319–1330

Citation in format AMSBIB

\Bibitem{RozSho08}

\by U.~A.~Rozikov, Sh.~A.~Shoyusupov

\paper Fertile HC models with three states on a~Cayley tree

\jour TMF

\yr 2008

\vol 156

\issue 3

\pages 412--424

\mathnet{http://mi.mathnet.ru/tmf6256}

\crossref{https://doi.org/10.4213/tmf6256}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2490265}

\zmath{https://zbmath.org/?q=an:1157.82312}

\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2008TMP...156.1319R}

\transl

\jour Theoret. and Math. Phys.

\yr 2008

\vol 156

\issue 3

\pages 1319--1330

\crossref{https://doi.org/10.1007/s11232-008-0109-5}

\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000259821400007}

\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-53349173709}

Linking options:

https://www.mathnet.ru/eng/tmf6256

https://doi.org/10.4213/tmf6256

https://www.mathnet.ru/eng/tmf/v156/i3/p412

This publication is cited in the following 24 articles:

B. Z. Tozhiboev, R. M. Khakimov, “Mery Gibbsa dlya $\mathrm{HC}$ -modeli v sluchae grafa tipa “klyuch” na dereve Keli”, Matem. zametki, 117:4 (2025), 575–590
N. M. Khatamov, “Periodic Gibbs Measures and Their Extremality for the HC-Blume–Capel Model in the Case of a Wand with a Chemical Potential on a Cayley Tree”, Math. Notes, 115:1 (2024), 89–101
Rustamjon Khakimov, Kamola Umirzakova, “Periodic Gibbs Measures for Three-State Hard-Core Models in the Case Wand”, Z. mat. fiz. anal. geom., 20:1 (2024), 66
R. M. Khakimov, B. Z. Tozhiboev, “Gibbs measures for fertile models with hard-core interactions and four states”, Theoret. and Math. Phys., 219:2 (2024), 823–838
Benedikt Jahnel, Utkir Rozikov, “Gibbs measures for hardcore-solid-on-solid models on Cayley trees”, J. Stat. Mech., 2024:7 (2024), 073202
Rustamjon Khakimov, Muhtorjon Makhammadaliev, Kamola Umirzakova, “Alternative Gibbs measure for fertile three-state Hard-Core models on a Cayley tree”, Phase Transitions, 2024, 1
R. M. Khakimov, M. T. Makhammadaliev, F. H. Haydarov, “New class of Gibbs measures for two-state hard-core model on a Cayley tree”, Infin. Dimens. Anal. Quantum. Probab. Relat. Top., 26:04 (2023)
N. M. Khatamov, “Extremality of Gibbs Measures for the $HC$ -Blume–Capel Model on the Cayley Tree”, Math. Notes, 111:5 (2022), 768–781
N. M. Khatamov, “Ekstremalnost nekotorykh mer Gibbsa dlya HC-modeli Blyuma-Kapelya na dereve Keli”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 32:2 (2022), 256–277
N. M. Khatamov, “Periodic Gibbs Measures and Their Extremes for the HC–Blume–Capel Model in the Case of a "Wand" on the Cayley Tree”, Lobachevskii J Math, 43:9 (2022), 2515
R. M. Khakimov, K. O. Umirzakova, “Extremality of the unique translation-invariant Gibbs measure for hard-core models on the Cayley tree of order $k=3$ ”, Theoret. and Math. Phys., 206:1 (2021), 97–108
R. M. Khakimov, M. T. Makhammadaliev, “Uniqueness and nonuniqueness conditions for weakly periodic Gibbs measures for the hard-core model”, Theoret. and Math. Phys., 204:2 (2020), 1059–1078
Kissel S. Kuelske C. Rozikov U.A., “Hard-Core and Soft-Core Widom-Rowlinson Models on Cayley Trees”, J. Stat. Mech.-Theory Exp., 2019, 043204
R. M. Khakimov, “Weakly periodic Gibbs measures for HC-models on Cayley trees”, Siberian Math. J., 59:1 (2018), 147–156
R. M. Khakimov, “Gibbs measures for fertile hard-core models on the Cayley tree”, Theoret. and Math. Phys., 186:2 (2016), 294–305
O. N. Khakimov, “A $p$ -adic hard-core model with three states on a Cayley tree”, Siberian Math. J., 57:4 (2016), 726–734
Gandolfo D. Rozikov U.A. Ruiz J., “on Four State Hard Core Models on the Cayley Tree”, Markov Process. Relat. Fields, 22:2 (2016), 359–377
R. M. Khakimov, “Weakly Periodic Gibbs Measures in the HC-Model for a Normal Divisor of Index Four”, Ukr Math J, 67:10 (2016), 1584
Rustam M. Khakimov, “The uniqueness of the translation-invariant Gibbs measure for four state HC-models on a Cayley tree”, Zhurn. SFU. Ser. Matem. i fiz., 8:2 (2015), 165–172
Rozikov U.A., Khakimov R.M., “Gibbs Measures For the Fertile Three-State Hard-Core Models on a Cayley Tree”, Queueing Syst., 81:1 (2015), 49–69

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

Statistics & downloads:
Abstract page:	482
Full-text PDF :	213
References:	72
First page:	2

Registration to the website

Logotypes