A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two

A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two

In the present paper, we introduce a new kind of p-adic measures for (q + 1)-state Potts model, called generalized p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. We employ a dynamical system approach to establish phase transition ph...

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Main Author: Mukhamedov, Farrukh
Format: Article
Language:English
Published: Elsevier 2012
Subjects:
QA Mathematics
QC Physics
Online Access:http://irep.iium.edu.my/28682/
http://irep.iium.edu.my/28682/
http://irep.iium.edu.my/28682/
http://irep.iium.edu.my/28682/1/mf-ROMP%282012%29.pdf
id iium-28682
recordtype eprints
spelling iium-286822013-02-13T09:42:01Z http://irep.iium.edu.my/28682/ A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two Mukhamedov, Farrukh QA Mathematics QC Physics In the present paper, we introduce a new kind of p-adic measures for (q + 1)-state Potts model, called generalized p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. We employ a dynamical system approach to establish phase transition phenomena for the given model. Namely, using the derived recursive relations we define a one-dimensional fractional p-adic dynamical system. We show that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. In this case, there exists a strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields the existence of a quasi phase transition. Elsevier 2012 Article PeerReviewed application/pdf en http://irep.iium.edu.my/28682/1/mf-ROMP%282012%29.pdf Mukhamedov, Farrukh (2012) A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two. Reports on Mathematical Physics, 70 (3). pp. 385-406. ISSN 00344877 http://dx.doi.org/10.1016/S0034-4877(12)60053-6 doi:10.1016/S0034-4877(12)60053-6
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
A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two
description In the present paper, we introduce a new kind of p-adic measures for (q + 1)-state Potts model, called generalized p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. We employ a dynamical system approach to establish phase transition phenomena for the given model. Namely, using the derived recursive relations we define a one-dimensional fractional p-adic dynamical system. We show that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. In this case, there exists a strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields the existence of a quasi phase transition.
format Article
author Mukhamedov, Farrukh
author_facet Mukhamedov, Farrukh
author_sort Mukhamedov, Farrukh
title A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two
title_short A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two
title_full A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two
title_fullStr A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two
title_full_unstemmed A dynamical system approach to phase transitions for p-adic Potts model on the Cayley tree of order two
title_sort dynamical system approach to phase transitions for p-adic potts model on the cayley tree of order two
publisher Elsevier
publishDate 2012
url http://irep.iium.edu.my/28682/
http://irep.iium.edu.my/28682/
http://irep.iium.edu.my/28682/
http://irep.iium.edu.my/28682/1/mf-ROMP%282012%29.pdf
first_indexed 2023-09-18T20:42:14Z
last_indexed 2023-09-18T20:42:14Z
_version_ 1777409441529856000

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