Modulated phase of a Potts Model with competing binary interactions on a Cayley tree
We study the phase diagram for Potts model on a Cayley tree with competing nearest-neighbor interactions J1, prolonged next-nearest-neighbor interactions Jp and one-level next-nearest-neighbor interactions Jo. Vannimenus proved that the phase diagram of Ising model with Jo=0 contains a modulated pha...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Springer Link
2009
|
| Subjects: | |
| Online Access: | http://irep.iium.edu.my/1639/ http://irep.iium.edu.my/1639/1/Modulated-phase-of-a-potts-model-with-competing-binary-interactions-on-a-cayley-tree_2009_Journal-of-Statistical-Physics.pdf |
| _version_ | 1848775889934876672 |
|---|---|
| author | Ganikhodjaev, Nasir Temir, Seyit Akin, Hasan |
| author_facet | Ganikhodjaev, Nasir Temir, Seyit Akin, Hasan |
| 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 nearest-neighbor interactions J1, prolonged next-nearest-neighbor interactions Jp and one-level next-nearest-neighbor interactions Jo. Vannimenus proved that the phase diagram of Ising model with Jo=0 contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature. Later Mariz et al. generalized this result for Ising model with Jo≠0 and recently Ganikhodjaev et al. proved similar result for the three-state Potts model with Jo=0. We consider Potts model with Jo≠0 and show that for some values of Jo the multicritical Lifshitz point be at non-zero temperature. We also prove that as soon as the same-level interactionJo is nonzero, the paramagnetic phase found at high temperatures for Jo=0 disappears, while Ising model does not obtain such property. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular case, previous work by Ganikhodjaev et al. for Jo=0. At vanishing temperature, the phase diagram is fully determined for all values and signs of J1,Jp and Jo. At finite temperatures several interesting features are exhibited for typical values of Jo/J1. |
| first_indexed | 2025-11-14T14:21:22Z |
| format | Article |
| id | iium-1639 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:22Z |
| publishDate | 2009 |
| publisher | Springer Link |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-16392011-09-05T08:38:59Z http://irep.iium.edu.my/1639/ Modulated phase of a Potts Model with competing binary interactions on a Cayley tree Ganikhodjaev, Nasir Temir, Seyit Akin, Hasan QA Mathematics We study the phase diagram for Potts model on a Cayley tree with competing nearest-neighbor interactions J1, prolonged next-nearest-neighbor interactions Jp and one-level next-nearest-neighbor interactions Jo. Vannimenus proved that the phase diagram of Ising model with Jo=0 contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature. Later Mariz et al. generalized this result for Ising model with Jo≠0 and recently Ganikhodjaev et al. proved similar result for the three-state Potts model with Jo=0. We consider Potts model with Jo≠0 and show that for some values of Jo the multicritical Lifshitz point be at non-zero temperature. We also prove that as soon as the same-level interactionJo is nonzero, the paramagnetic phase found at high temperatures for Jo=0 disappears, while Ising model does not obtain such property. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular case, previous work by Ganikhodjaev et al. for Jo=0. At vanishing temperature, the phase diagram is fully determined for all values and signs of J1,Jp and Jo. At finite temperatures several interesting features are exhibited for typical values of Jo/J1. Springer Link 2009 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1639/1/Modulated-phase-of-a-potts-model-with-competing-binary-interactions-on-a-cayley-tree_2009_Journal-of-Statistical-Physics.pdf Ganikhodjaev, Nasir and Temir, Seyit and Akin, Hasan (2009) Modulated phase of a Potts Model with competing binary interactions on a Cayley tree. Journal of Statistical Physics, 137 (4). pp. 701-715. ISSN 0022-4715 http://www.springerlink.com/content/102588/ 10.1007/s10955-009-9869-z |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Temir, Seyit Akin, Hasan Modulated phase of a Potts Model with competing binary interactions on a Cayley tree |
| title | Modulated phase of a Potts Model with competing binary interactions on a Cayley tree |
| title_full | Modulated phase of a Potts Model with competing binary interactions on a Cayley tree |
| title_fullStr | Modulated phase of a Potts Model with competing binary interactions on a Cayley tree |
| title_full_unstemmed | Modulated phase of a Potts Model with competing binary interactions on a Cayley tree |
| title_short | Modulated phase of a Potts Model with competing binary interactions on a Cayley tree |
| title_sort | modulated phase of a potts model with competing binary interactions on a cayley tree |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/1639/ http://irep.iium.edu.my/1639/ http://irep.iium.edu.my/1639/ http://irep.iium.edu.my/1639/1/Modulated-phase-of-a-potts-model-with-competing-binary-interactions-on-a-cayley-tree_2009_Journal-of-Statistical-Physics.pdf |