Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree

In this present paper, we consider the p-adic Ising Vannimenus model on the Cayley tree of order two. A new measure-theoretical approach (in the p-adic sense) to investigate such a model is proposed. The main result of this paper is to establish the existence of the phase transition for the model. B...

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Main Authors:	Mukhamedov, Farrukh, Dogan, Mutlay, Akin, Hasan
Format:	Article
Language:	English English
Published:	IOP Publishing Ltd. 2014
Subjects:	QA Mathematics QC Physics
Online Access:	http://irep.iium.edu.my/38902/ http://irep.iium.edu.my/38902/ http://irep.iium.edu.my/38902/ http://irep.iium.edu.my/38902/1/mfmdha-JSTAT%282014%29.pdf http://irep.iium.edu.my/38902/4/38902_Phase%20transition_scopus_new.pdf

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recordtype	eprints
spelling	iium-389022017-09-25T07:47:50Z http://irep.iium.edu.my/38902/ Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree Mukhamedov, Farrukh Dogan, Mutlay Akin, Hasan QA Mathematics QC Physics In this present paper, we consider the p-adic Ising Vannimenus model on the Cayley tree of order two. A new measure-theoretical approach (in the p-adic sense) to investigate such a model is proposed. The main result of this paper is to establish the existence of the phase transition for the model. By the phase transition we mean the existence of at least two non-trivial p-adic quasi Gibbs measures, such that one is bounded and the second one is unbounded (note that in the p-adic probability, unlike a real setting, the probability measures could even be unbounded). To prove the main result, we investigate a nonlinear recurrence equation via the methods of p-adic analysis. Note that the methods used in the paper are not valid in a real setting IOP Publishing Ltd. 2014-10 Article PeerReviewed application/pdf en http://irep.iium.edu.my/38902/1/mfmdha-JSTAT%282014%29.pdf application/pdf en http://irep.iium.edu.my/38902/4/38902_Phase%20transition_scopus_new.pdf Mukhamedov, Farrukh and Dogan, Mutlay and Akin, Hasan (2014) Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree. Journal of Statistical Mechanics: Theory and Experiment, 2014 (10). ISSN 1742-5468 http://dx.doi.org/10.1088/1742-5468/2014/10/P10031 doi:10.1088/1742-5468/2014/10/P10031
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English
topic	QA Mathematics QC Physics
spellingShingle	QA Mathematics QC Physics Mukhamedov, Farrukh Dogan, Mutlay Akin, Hasan Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree
description	In this present paper, we consider the p-adic Ising Vannimenus model on the Cayley tree of order two. A new measure-theoretical approach (in the p-adic sense) to investigate such a model is proposed. The main result of this paper is to establish the existence of the phase transition for the model. By the phase transition we mean the existence of at least two non-trivial p-adic quasi Gibbs measures, such that one is bounded and the second one is unbounded (note that in the p-adic probability, unlike a real setting, the probability measures could even be unbounded). To prove the main result, we investigate a nonlinear recurrence equation via the methods of p-adic analysis. Note that the methods used in the paper are not valid in a real setting
format	Article
author	Mukhamedov, Farrukh Dogan, Mutlay Akin, Hasan
author_facet	Mukhamedov, Farrukh Dogan, Mutlay Akin, Hasan
author_sort	Mukhamedov, Farrukh
title	Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree
title_short	Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree
title_full	Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree
title_fullStr	Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree
title_full_unstemmed	Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree
title_sort	phase transition for the p-adic ising–vannimenus model on the cayley tree
publisher	IOP Publishing Ltd.
publishDate	2014
url	http://irep.iium.edu.my/38902/ http://irep.iium.edu.my/38902/ http://irep.iium.edu.my/38902/ http://irep.iium.edu.my/38902/1/mfmdha-JSTAT%282014%29.pdf http://irep.iium.edu.my/38902/4/38902_Phase%20transition_scopus_new.pdf
first_indexed	2023-09-18T20:55:53Z
last_indexed	2023-09-18T20:55:53Z
_version_	1777410301225861120

Phase transition for the p-adic Ising–Vannimenus model on the Cayley tree

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