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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| Format: | Article |
| Language: | English |
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Elsevier
2012
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| Online Access: | http://irep.iium.edu.my/28682/ http://irep.iium.edu.my/28682/1/mf-ROMP%282012%29.pdf |
| _version_ | 1848780002121744384 |
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| author | Mukhamedov, Farrukh |
| author_facet | Mukhamedov, Farrukh |
| author_sort | Mukhamedov, Farrukh |
| building | IIUM Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-14T15:26:44Z |
| format | Article |
| id | iium-28682 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T15:26:44Z |
| publishDate | 2012 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| 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 |
| 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 |
| title | 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_short | 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 |
| topic | QA Mathematics QC Physics |
| 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 |