Existence of phase transition for 1d-countable state P -adic Potts model

In the present paper we shall consider countable state p -adic Potts model on Z . A main aim is to establish the existence of the phase transition for the model. In our study, we essentially use one dimensionality of the model. The existence of the phase transition is reduced to the investigation o...

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Main Author:	Mukhamedov, Farrukh
Format:	Book Chapter
Language:	English
Published:	ASR MATBUOT” ltd. 2012
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/26068/ http://irep.iium.edu.my/26068/1/mf-Proc-Turin2012.pdf

id	iium-26068
recordtype	eprints
spelling	iium-260682012-12-31T03:40:56Z http://irep.iium.edu.my/26068/ Existence of phase transition for 1d-countable state P -adic Potts model Mukhamedov, Farrukh QA Mathematics In the present paper we shall consider countable state p -adic Potts model on Z . A main aim is to establish the existence of the phase transition for the model. In our study, we essentially use one dimensionality of the model. The existence of the phase transition is reduced to the investigation of an infinitedimensional nonlinear equation. We find a condition on weights to show that the derived equation has two solutions, which yields the existence of the phase transition. We prove that measures corresponding to first and second solutions are a p -adic Gibbs and generalized p -adic Gibbs measures, respectively. Note that it turns out that the finding condition does not depend on values of the prime p , and therefore, an analogous fact is not true when the number of spins is finite ASR MATBUOT” ltd. 2012 Book Chapter PeerReviewed application/pdf en http://irep.iium.edu.my/26068/1/mf-Proc-Turin2012.pdf Mukhamedov, Farrukh (2012) Existence of phase transition for 1d-countable state P -adic Potts model. In: Proceedings of Turin Polytechnic University in Tashkent. ASR MATBUOT” ltd., Tashkent, Uzbekistan, pp. 228-242.
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics
spellingShingle	QA Mathematics Mukhamedov, Farrukh Existence of phase transition for 1d-countable state P -adic Potts model
description	In the present paper we shall consider countable state p -adic Potts model on Z . A main aim is to establish the existence of the phase transition for the model. In our study, we essentially use one dimensionality of the model. The existence of the phase transition is reduced to the investigation of an infinitedimensional nonlinear equation. We find a condition on weights to show that the derived equation has two solutions, which yields the existence of the phase transition. We prove that measures corresponding to first and second solutions are a p -adic Gibbs and generalized p -adic Gibbs measures, respectively. Note that it turns out that the finding condition does not depend on values of the prime p , and therefore, an analogous fact is not true when the number of spins is finite
format	Book Chapter
author	Mukhamedov, Farrukh
author_facet	Mukhamedov, Farrukh
author_sort	Mukhamedov, Farrukh
title	Existence of phase transition for 1d-countable state P -adic Potts model
title_short	Existence of phase transition for 1d-countable state P -adic Potts model
title_full	Existence of phase transition for 1d-countable state P -adic Potts model
title_fullStr	Existence of phase transition for 1d-countable state P -adic Potts model
title_full_unstemmed	Existence of phase transition for 1d-countable state P -adic Potts model
title_sort	existence of phase transition for 1d-countable state p -adic potts model
publisher	ASR MATBUOT” ltd.
publishDate	2012
url	http://irep.iium.edu.my/26068/ http://irep.iium.edu.my/26068/1/mf-Proc-Turin2012.pdf
first_indexed	2023-09-18T20:38:52Z
last_indexed	2023-09-18T20:38:52Z
_version_	1777409230200897536

Existence of phase transition for 1d-countable state P -adic Potts model

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