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

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Mat. Fiz. Anal. Geom.:
Year:
Volume:
Issue:
Page:
Find






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


Zh. Mat. Fiz. Anal. Geom., 2016, Volume 12, Number 4, Pages 302–314 (Mi jmag655)  

On weakly periodic Gibbs measures of the Potts model with a special external field on a Cayley tree

M. M. Rahmatullaev

Institut of Mathematics, 29 Durmon Yuli Str., 100125, Uzbekistan

Abstract: In the paper, we study the $q$-state (where $q=3,4,5,…$) Potts model with special external field on a Cayley tree of order $k\geq 2$. For antiferromagnetic Potts model with such an external field on the Cayley tree of order $k\geq 6$, the non-uniqueness of weakly periodic (non-periodic) Gibbs measures is proved. The weakly periodic Gibbs measures for the Potts model with zero external field are also studied. It is proved that under some conditions imposed on the parameters of the model there can be not less than $2^q-2$ such measures.

Key words and phrases: Cayley tree, Gibbs measure, Potts model, weakly periodic measure.

DOI: https://doi.org/10.15407/mag12.04.302      

Full text: PDF file (192 kB)
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 82B26; Secondary 60K35
Received: 05.03.2015
Revised: 27.01.2016
Language:

Citation: M. M. Rahmatullaev, “On weakly periodic Gibbs measures of the Potts model with a special external field on a Cayley tree”, Zh. Mat. Fiz. Anal. Geom., 12:4 (2016), 302–314

Citation in format AMSBIB
\Bibitem{Rah16}
\by M.~M.~Rahmatullaev
\paper On weakly periodic Gibbs measures of the Potts model with a special external field on a Cayley tree
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2016
\vol 12
\issue 4
\pages 302--314
\mathnet{http://mi.mathnet.ru/jmag655}
\crossref{https://doi.org/10.15407/mag12.04.302  }
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3583326}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000392861500002}


Linking options:
  • http://mi.mathnet.ru/eng/jmag655
  • http://mi.mathnet.ru/eng/jmag/v12/i4/p302

    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
  • Number of views:
    This page:91
    Full text:24
    References:16

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020