On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree
In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider twomode of interactions: ferromagnetic and antiferromagnetic. I...
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| Format: | Article |
| Language: | English |
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Springer Netherlands
2013
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| Online Access: | http://irep.iium.edu.my/29716/1/mf-MPAG%282013%29.pdf |
| _version_ | 1796877964615352320 |
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| author | Mukhamedov, Farrukh |
| author_facet | Mukhamedov, Farrukh |
| author_sort | Mukhamedov, Farrukh |
| collection | IIUM |
| description | In the present paper, we study a new kind of p-adic measures for
q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model,
we derive a recursive relations with respect to boundary conditions. Note that
we consider twomode of interactions: ferromagnetic and antiferromagnetic. In
both cases, we investigate a phase transition phenomena from the associated
dynamical system point of view. Namely, using the derived recursive relations
we define a fractional p-adic dynamical system. In ferromagnetic case, we
establish that if q is divisible by p, then such a dynamical system has two
repelling and one attractive fixed points. We find basin of attraction of the
fixed point. This allows us to describe all solutions of the nonlinear recursive
equations. Moreover, in that case there exists the strong phase transition. If
q is not divisible by p, then the fixed points are neutral, and this yields that
the existence of the quasi phase transition. In antiferromagnetic case, there
are two attractive fixed points, and we find basins of attraction of both fixed
points, and describe solutions of the nonlinear recursive equation. In this case,
we prove the existence of a quasi phase transition. |
| first_indexed | 2024-03-05T23:14:48Z |
| format | Article |
| id | oai:generic.eprints.org:29716 |
| institution | International Islamic University Malaysia |
| language | English |
| last_indexed | 2024-03-05T23:14:48Z |
| publishDate | 2013 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | oai:generic.eprints.org:297162013-04-23T07:22:05Z http://irep.iium.edu.my/29716/ On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree Mukhamedov, Farrukh QA Mathematics In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider twomode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition. Springer Netherlands 2013 Article PeerReviewed application/pdf en http://irep.iium.edu.my/29716/1/mf-MPAG%282013%29.pdf Mukhamedov, Farrukh (2013) On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree. Mathematical Physics, Analysis and Geometry, 16 (1). pp. 49-87. ISSN 1385-0172 (P), 1572-9656 (O) http://link.springer.com/article/10.1007%2Fs11040-012-9120-z 10.1007/s11040-012-9120-z |
| spellingShingle | QA Mathematics Mukhamedov, Farrukh On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree |
| title | On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree |
| title_full | On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree |
| title_fullStr | On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree |
| title_full_unstemmed | On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree |
| title_short | On dynamical systems and phase transitions for q + 1-state p-adic Potts model on the Cayley tree |
| title_sort | on dynamical systems and phase transitions for q 1 state p adic potts model on the cayley tree |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/29716/1/mf-MPAG%282013%29.pdf |
| work_keys_str_mv | AT mukhamedovfarrukh ondynamicalsystemsandphasetransitionsforq1statepadicpottsmodelonthecayleytree |