Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions
We study the phase diagram for Potts model on a Cayley tree with competing nearestneighbor interactions J1, prolonged next-nearest-neighbor interactions J2 and one-level nextnearest- neighbor interactions J3. Vannimenus [1] proved that the phase diagram of Ising model with Jo = 0 contains a modulate...
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| Format: | Proceeding Paper |
| Language: | English |
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EUDOXUS PRESS, LLC
2010
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| Online Access: | http://irep.iium.edu.my/1689/ http://irep.iium.edu.my/1689/1/abstract_CCS_2010.pdf |
| _version_ | 1848775900554854400 |
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| author | Ganikhodjaev, Nasir |
| author_facet | Ganikhodjaev, Nasir |
| author_sort | Ganikhodjaev, Nasir |
| building | IIUM Repository |
| collection | Online Access |
| description | We study the phase diagram for Potts model on a Cayley tree with competing nearestneighbor interactions J1, prolonged next-nearest-neighbor interactions J2 and one-level nextnearest- neighbor interactions J3. Vannimenus [1] proved that the phase diagram of Ising model with Jo = 0 contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al [2] generalized this result for Ising model with Jo 6= 0 and recently anikhodjaev et al [3] proved similar result for the three-state Potts model with Jo = 0. For given lattice model on a Cayley tree we produce recursive relations obtained following the lines of Inawashiro et al [4]. These recursive relations provide us the numerically exact phase
diagram of the model. Each phase is characterized by a particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several interesting features (evolution of reentrances, separation
of the modulated region into few disconnected pieces, etc) are exhibited for typical values of J2/J1, J3/J1. |
| first_indexed | 2025-11-14T14:21:33Z |
| format | Proceeding Paper |
| id | iium-1689 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:33Z |
| publishDate | 2010 |
| publisher | EUDOXUS PRESS, LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-16892011-12-12T02:55:06Z http://irep.iium.edu.my/1689/ Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions Ganikhodjaev, Nasir QA Mathematics We study the phase diagram for Potts model on a Cayley tree with competing nearestneighbor interactions J1, prolonged next-nearest-neighbor interactions J2 and one-level nextnearest- neighbor interactions J3. Vannimenus [1] proved that the phase diagram of Ising model with Jo = 0 contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al [2] generalized this result for Ising model with Jo 6= 0 and recently anikhodjaev et al [3] proved similar result for the three-state Potts model with Jo = 0. For given lattice model on a Cayley tree we produce recursive relations obtained following the lines of Inawashiro et al [4]. These recursive relations provide us the numerically exact phase diagram of the model. Each phase is characterized by a particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into few disconnected pieces, etc) are exhibited for typical values of J2/J1, J3/J1. EUDOXUS PRESS, LLC 2010-05-24 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/1689/1/abstract_CCS_2010.pdf Ganikhodjaev, Nasir (2010) Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions. In: 3rd International Interdisciplinary Chaos Symposium on Chaos and Complex Systems, 21-24 May 2010, Istanbul, Turkey. (Unpublished) http://www.iku.edu.tr/TR/semp_icerik.php?p=159&r=0 |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions |
| title | Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions |
| title_full | Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions |
| title_fullStr | Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions |
| title_full_unstemmed | Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions |
| title_short | Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions |
| title_sort | strange attractor in the potts model on a cayley tree in the presence of competing interactions |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/1689/ http://irep.iium.edu.my/1689/ http://irep.iium.edu.my/1689/1/abstract_CCS_2010.pdf |