RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Subscription
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


TMF, 1999, Volume 118, Number 1, Pages 95–104 (Mi tmf688)  

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

Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model

U. A. Rozikov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We prove the existence of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model on a Cayley tree and describe them constructively.

DOI: https://doi.org/10.4213/tmf688

Full text: PDF file (229 kB)
References: PDF file   HTML file

English version:
Theoretical and Mathematical Physics, 1999, 118:1, 77–84

Bibliographic databases:

Received: 11.03.1998
Revised: 04.06.1998

Citation: U. A. Rozikov, “Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model”, TMF, 118:1 (1999), 95–104; Theoret. and Math. Phys., 118:1 (1999), 77–84

Citation in format AMSBIB
\Bibitem{Roz99}
\by U.~A.~Rozikov
\paper Construction of an uncountable number of limiting Gibbs measures in the inhomogeneous Ising model
\jour TMF
\yr 1999
\vol 118
\issue 1
\pages 95--104
\mathnet{http://mi.mathnet.ru/tmf688}
\crossref{https://doi.org/10.4213/tmf688}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1702836}
\zmath{https://zbmath.org/?q=an:0957.82007}
\transl
\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
\issue 1
\pages 77--84
\crossref{https://doi.org/10.1007/BF02557197}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000079262300007}


Linking options:
  • http://mi.mathnet.ru/eng/tmf688
  • https://doi.org/10.4213/tmf688
  • http://mi.mathnet.ru/eng/tmf/v118/i1/p95

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


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

    This publication is cited in the following articles:
    1. A. M. Rakhmatullaev, U. A. Rozikov, “Gibbs Measures and Markov Random Fields with Association $I$”, Math. Notes, 72:1 (2002), 83–89  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. U. A. Rozikov, “Countably Periodic Gibbs Measures of the Ising Model on the Cayley Tree”, Theoret. and Math. Phys., 130:1 (2002), 92–100  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. N. N. Ganikhodzhaev, F. M. Mukhamedov, U. A. Rozikov, “$\mathbb {Z}$Existence of a Phase Transition for the Potts $p$-adic Model on the Set $\mathbb {Z}$”, Theoret. and Math. Phys., 130:3 (2002), 425–431  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. U. A. Rozikov, “Representability of Trees and Some of Their Applications”, Math. Notes, 72:4 (2002), 479–488  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. Kh. A. Nazarov, U. A. Rozikov, “Periodic Gibbs Measures for the Ising Model with Competing Interactions”, Theoret. and Math. Phys., 135:3 (2003), 881–888  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. N. N. Ganikhodzhaev, U. A. Rozikov, “Group representation of the Cayley forest and some of its applications”, Izv. Math., 67:1 (2003), 17–27  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. Mukhamedov F, Rozikov U, “On Gibbs measures of models with competing ternary and binary interactions and corresponding von Neumann algebras”, Journal of Statistical Physics, 114:3–4 (2004), 825–848  crossref  mathscinet  zmath  adsnasa  isi
    8. Suhov, Y, “A hard-core model on a Cayley tree: An example of a loss network”, Queueing Systems, 46:1–2 (2004), 197  crossref  mathscinet  zmath  isi
    9. Martin, J, “A three state hard-core model on a Cayley tree”, Journal of Nonlinear Mathematical Physics, 12:3 (2005), 432  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    10. É. P. Normatov, U. A. Rozikov, “A description of harmonic functions via properties of the group representation of the Cayley tree”, Math. Notes, 79:3 (2006), 399–407  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. Rozikov, UA, “Gibbs measures for SOS models on a Cayley tree”, Infinite Dimensional Analysis Quantum Probability and Related Topics, 9:3 (2006), 471  crossref  mathscinet  zmath  isi  scopus  scopus
    12. U. A. Rozikov, Sh. A. Shoyusupov, “Gibbs measures for the SOS model with four states on a Cayley tree”, Theoret. and Math. Phys., 149:1 (2006), 1312–1323  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. U. A. Rozikov, M. M. Rakhmatullaev, “Description of weakly periodic Gibbs measures for the Ising model on a Cayley tree”, Theoret. and Math. Phys., 156:2 (2008), 1218–1227  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    14. U. A. Rozikov, Sh. A. Shoyusupov, “Fertile HC models with three states on a Cayley tree”, Theoret. and Math. Phys., 156:3 (2008), 1319–1330  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    15. Ganikhodjaev, NN, “On Ising Model with Four Competing Interactions on Cayley Tree”, Mathematical Physics Analysis and Geometry, 12:2 (2009), 141  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    16. U. A. Rozikov, G. T. Madgoziev, “Nonuniqueness of a Gibbs measure for a model on the Cayley tree”, Theoret. and Math. Phys., 167:2 (2011), 668–679  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    17. Rozikov U.A., “Gibbs Measures on Cayley Trees: Results and Open Problems”, Rev. Math. Phys., 25:1 (2013), 1330001  crossref  mathscinet  isi  elib  scopus  scopus  scopus
    18. N. M. Khatamov, “Nonuniqueness of a Gibbs measure for the Ising ball model”, Theoret. and Math. Phys., 180:3 (2014), 1030–1039  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    19. N. M. Khatamov, G. T. Madgoziev, “Gibbs measures for a generalized Potts model with the interaction radius two on a Cayley tree”, Theoret. and Math. Phys., 183:3 (2015), 836–845  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    20. M. M. Rakhmatullaev, “Weakly periodic Gibbs measures of the Ising model with an external field on the Cayley tree”, Theoret. and Math. Phys., 183:3 (2015), 822–828  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    21. M. M. Rakhmatullaev, “New weakly periodic Gibbs measures of Ising model on Cayley tree”, Russian Math. (Iz. VUZ), 59:11 (2015), 45–53  mathnet  crossref
    22. Albeverio S. Omirov B.A. Rozikov U.A., “Periodic Algebras Generated By Groups”, Algebr. Colloq., 22:4 (2015), 541–554  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    23. Rahmatullaev M., “On new weakly periodic Gibbs measures of the Ising model on the Cayley tree of order ? 5”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, ed. Ayupov S. Chilin V. Ganikhodjaev N. Mukhamedov F. Rakhimov I., IOP Publishing Ltd, 2016, 012020  crossref  isi  scopus
    24. Ganikhodjaev N. Rahmatullaev M. Rodzhan Mohd Hirzie Bin Mohd, “Weakly Periodic Gibbs Measures of the Ising Model on the Cayley Tree of Order Five and Six”, Math. Phys. Anal. Geom., 21:1 (2017), 2  crossref  mathscinet  isi  scopus  scopus  scopus
    25. Bissacot R., Endo E.O., van Enter A.C.D., “Stability of the Phase Transition of Critical-Field Ising Model on Cayley Trees Under Inhomogeneous External Fields”, Stoch. Process. Their Appl., 127:12 (2017), 4126–4138  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    26. Rahmatullaev M., “Ising Model on Trees: (K(0)) - Non Translation-Invariant Gibbs Measures”, 37Th International Conference on Quantum Probability and Related Topics (Qp37), Journal of Physics Conference Series, 819, ed. Accardi L. Mukhamedov F. Hee P., IOP Publishing Ltd, 2017, UNSP 012019  crossref  mathscinet  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
    Number of views:
    This page:209
    Full text:79
    References:21
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019