On the strong phase transition for the one-dimensional countable statep-adic Potts model

In the present paper we consider the countable state p-adic Potts model on Z+. A main aim is to establish the existence of the strong phase transition for the model. In our study, we essentially use one dimensionality of the model. To prove the existence of the phase transition, we reduce the pr...

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Main Author: Mukhamedov, Farrukh
Format: Article
Language:English
Published: Institute of Physics Publishing Ltd. 2014
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Online Access:http://irep.iium.edu.my/35681/
http://irep.iium.edu.my/35681/
http://irep.iium.edu.my/35681/
http://irep.iium.edu.my/35681/1/mf-JSTAT%282014%29.pdf
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spelling iium-356812014-02-19T03:12:08Z http://irep.iium.edu.my/35681/ On the strong phase transition for the one-dimensional countable statep-adic Potts model Mukhamedov, Farrukh QA Mathematics QC Physics In the present paper we consider the countable state p-adic Potts model on Z+. A main aim is to establish the existence of the strong phase transition for the model. In our study, we essentially use one dimensionality of the model. To prove the existence of the phase transition, we reduce the problem to the investigation of an in�nite-dimensional nonlinear equation. We �nd a condition on weights to show that the derived equation has two solutions. We show that measures corresponding to �rst and second solutions are a p-adic Gibbs and generalized p-adic Gibbs measures, respectively. Moreover, it is proved that the p-adic Gibbs measure is bounded, and the generalized one is not bounded. This implies the existence of the strong phase transition. Note that it turns out that the obtained condition does not depend on values of the prime p and, therefore, an analogous fact is not true when the number of spins is �nite. Note that, in the usual real case, if one considers a one-dimensional translation- invariant model with nearest neighbor interaction, then such a model does not exhibit a phase transition. Nevertheless, we should stress that our model exhibits a unique p-adic Gibbs measure. Institute of Physics Publishing Ltd. 2014 Article PeerReviewed application/pdf en http://irep.iium.edu.my/35681/1/mf-JSTAT%282014%29.pdf Mukhamedov, Farrukh (2014) On the strong phase transition for the one-dimensional countable statep-adic Potts model. Journal of Statistical Mechanics: Theory and Experiment, 2014 (P01007). pp. 1-23. ISSN 1742-5468 (O) http://dx.doi.org/10.1088/1742-5468/2014/01/P01007 doi:10.1088/1742-5468/2014/01/P01007
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
On the strong phase transition for the one-dimensional countable statep-adic Potts model
description In the present paper we consider the countable state p-adic Potts model on Z+. A main aim is to establish the existence of the strong phase transition for the model. In our study, we essentially use one dimensionality of the model. To prove the existence of the phase transition, we reduce the problem to the investigation of an in�nite-dimensional nonlinear equation. We �nd a condition on weights to show that the derived equation has two solutions. We show that measures corresponding to �rst and second solutions are a p-adic Gibbs and generalized p-adic Gibbs measures, respectively. Moreover, it is proved that the p-adic Gibbs measure is bounded, and the generalized one is not bounded. This implies the existence of the strong phase transition. Note that it turns out that the obtained condition does not depend on values of the prime p and, therefore, an analogous fact is not true when the number of spins is �nite. Note that, in the usual real case, if one considers a one-dimensional translation- invariant model with nearest neighbor interaction, then such a model does not exhibit a phase transition. Nevertheless, we should stress that our model exhibits a unique p-adic Gibbs measure.
format Article
author Mukhamedov, Farrukh
author_facet Mukhamedov, Farrukh
author_sort Mukhamedov, Farrukh
title On the strong phase transition for the one-dimensional countable statep-adic Potts model
title_short On the strong phase transition for the one-dimensional countable statep-adic Potts model
title_full On the strong phase transition for the one-dimensional countable statep-adic Potts model
title_fullStr On the strong phase transition for the one-dimensional countable statep-adic Potts model
title_full_unstemmed On the strong phase transition for the one-dimensional countable statep-adic Potts model
title_sort on the strong phase transition for the one-dimensional countable statep-adic potts model
publisher Institute of Physics Publishing Ltd.
publishDate 2014
url http://irep.iium.edu.my/35681/
http://irep.iium.edu.my/35681/
http://irep.iium.edu.my/35681/
http://irep.iium.edu.my/35681/1/mf-JSTAT%282014%29.pdf
first_indexed 2023-09-18T20:51:08Z
last_indexed 2023-09-18T20:51:08Z
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