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On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model

We consider the one-dimensional countable state p-adic Potts model. A construction of generalized p-adic Gibbs measures depending on weights λ is given, and an investigation of such measures is reduced to the examination of a p-adic dynamical system. This dynamical system has a form of series of ra...

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Main Author: Mukhamedov, Farrukh
Format: Article
Language:English
Published: Pleiades Publishing, Ltd. & Springer 2009
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/13695/1/mf-ProcMIRAN%282009%29.pdf
http://irep.iium.edu.my/13695/
http://www.springerlink.com/content/5303167707026682/
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spelling my.iium.irep.136952012-01-03T03:03:54Z http://irep.iium.edu.my/13695/ On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model Mukhamedov, Farrukh QA Mathematics We consider the one-dimensional countable state p-adic Potts model. A construction of generalized p-adic Gibbs measures depending on weights λ is given, and an investigation of such measures is reduced to the examination of a p-adic dynamical system. This dynamical system has a form of series of rational functions. Studying such a dynamical system, under some condition concerning weights, we prove the existence of generalized p-adic Gibbs measures. Note that the condition found does not depend on the values of the prime p, and therefore an analogous fact is not true when the number of states is finite. It is also shown that under the condition there may occur a phase transition. Pleiades Publishing, Ltd. & Springer 2009 Article REM application/pdf en http://irep.iium.edu.my/13695/1/mf-ProcMIRAN%282009%29.pdf Mukhamedov, Farrukh (2009) On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model. Proceedings of the Steklov Institute of Mathematics, 265 (1). pp. 165-176. ISSN 0081-5438 http://www.springerlink.com/content/5303167707026682/ 10.1134/S0081543809020163
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Mukhamedov, Farrukh
On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model
description We consider the one-dimensional countable state p-adic Potts model. A construction of generalized p-adic Gibbs measures depending on weights λ is given, and an investigation of such measures is reduced to the examination of a p-adic dynamical system. This dynamical system has a form of series of rational functions. Studying such a dynamical system, under some condition concerning weights, we prove the existence of generalized p-adic Gibbs measures. Note that the condition found does not depend on the values of the prime p, and therefore an analogous fact is not true when the number of states is finite. It is also shown that under the condition there may occur a phase transition.
format Article
author Mukhamedov, Farrukh
author_facet Mukhamedov, Farrukh
author_sort Mukhamedov, Farrukh
title On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model
title_short On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model
title_full On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model
title_fullStr On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model
title_full_unstemmed On the existence of generalized Gibbs measures for the one-dimensional p-adic countable state Potts model
title_sort on the existence of generalized gibbs measures for the one-dimensional p-adic countable state potts model
publisher Pleiades Publishing, Ltd. & Springer
publishDate 2009
url http://irep.iium.edu.my/13695/1/mf-ProcMIRAN%282009%29.pdf
http://irep.iium.edu.my/13695/
http://www.springerlink.com/content/5303167707026682/
_version_ 1643606786955018240
score 13.18916

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