On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree

On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree

In this paper, we continue an investigation of the p-adic Ising– Vannimenus model on the Cayley tree of an arbitrary order k (k > 2). We prove the existence of p-adic quasi Gibbs measures by analyzing fixed points of multidimensional p-adic system of equations. We are also able to show the uni...

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Main Authors: Mukhamedov, Farrukh, Saburov, Mansoor, Khakimov, Otabek
Format: Article
Language:English
Published: Institute of Physics Publishing Ltd. 2015
Subjects:
QA Mathematics
QC Physics
Online Access:http://irep.iium.edu.my/44018/
http://irep.iium.edu.my/44018/
http://irep.iium.edu.my/44018/
http://irep.iium.edu.my/44018/1/mfmsokh-jstat-2015.pdf
id iium-44018
recordtype eprints
spelling iium-440182019-04-09T02:03:41Z http://irep.iium.edu.my/44018/ On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree Mukhamedov, Farrukh Saburov, Mansoor Khakimov, Otabek QA Mathematics QC Physics In this paper, we continue an investigation of the p-adic Ising– Vannimenus model on the Cayley tree of an arbitrary order k (k > 2). We prove the existence of p-adic quasi Gibbs measures by analyzing fixed points of multidimensional p-adic system of equations. We are also able to show the uniqueness of translation-invariant p-adic Gibbs measure. Finally, it is established the existence of the phase transition for the Ising–Vannimenus model depending on the order k of the Cayley tree and the prime p. Note that the methods used in the paper are not valid in the real setting, since all of them are based on p-adic analysis and p-adic probability measures. Institute of Physics Publishing Ltd. 2015-05 Article PeerReviewed application/pdf en http://irep.iium.edu.my/44018/1/mfmsokh-jstat-2015.pdf Mukhamedov, Farrukh and Saburov, Mansoor and Khakimov, Otabek (2015) On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree. Journal of Statistical Mechanics: Theory and Experiment, 2015 (5). P05032. ISSN 1742-5468 (O) http://dx.doi.org/10.1088/1742-5468/2015/05/P05032 10.1088/1742-5468/2015/05/P05032
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
QC Physics
spellingShingle QA Mathematics
QC Physics
Mukhamedov, Farrukh
Saburov, Mansoor
Khakimov, Otabek
On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree
description In this paper, we continue an investigation of the p-adic Ising– Vannimenus model on the Cayley tree of an arbitrary order k (k > 2). We prove the existence of p-adic quasi Gibbs measures by analyzing fixed points of multidimensional p-adic system of equations. We are also able to show the uniqueness of translation-invariant p-adic Gibbs measure. Finally, it is established the existence of the phase transition for the Ising–Vannimenus model depending on the order k of the Cayley tree and the prime p. Note that the methods used in the paper are not valid in the real setting, since all of them are based on p-adic analysis and p-adic probability measures.
format Article
author Mukhamedov, Farrukh
Saburov, Mansoor
Khakimov, Otabek
author_facet Mukhamedov, Farrukh
Saburov, Mansoor
Khakimov, Otabek
author_sort Mukhamedov, Farrukh
title On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree
title_short On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree
title_full On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree
title_fullStr On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree
title_full_unstemmed On p-adic Ising–Vannimenus model on an arbitrary order Cayley tree
title_sort on p-adic ising–vannimenus model on an arbitrary order cayley tree
publisher Institute of Physics Publishing Ltd.
publishDate 2015
url http://irep.iium.edu.my/44018/
http://irep.iium.edu.my/44018/
http://irep.iium.edu.my/44018/
http://irep.iium.edu.my/44018/1/mfmsokh-jstat-2015.pdf
first_indexed 2023-09-18T21:02:37Z
last_indexed 2023-09-18T21:02:37Z
_version_ 1777410723872243712

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