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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Pleiades Publishing, Ltd. & Springer
2009
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| Online Access: | http://irep.iium.edu.my/13695/ http://irep.iium.edu.my/13695/ http://irep.iium.edu.my/13695/ http://irep.iium.edu.my/13695/1/mf-ProcMIRAN%282009%29.pdf |
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iium-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 PeerReviewed 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 |
| 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 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/ http://irep.iium.edu.my/13695/ http://irep.iium.edu.my/13695/ http://irep.iium.edu.my/13695/1/mf-ProcMIRAN%282009%29.pdf |
| first_indexed |
2023-09-18T20:22:49Z |
| last_indexed |
2023-09-18T20:22:49Z |
| _version_ |
1777408220202008576 |