Phase diagram of the Ising model with next-nearest-neighbour interactions
We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jp and one-level next-nearest neighbour interactions J0. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1 and prolonged next-nearest...
| Main Authors: | , |
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| Format: | Book Chapter |
| Language: | English |
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Faculty of Engineering, International Islamic University Malaysia (IIUM)
2010
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| Online Access: | http://irep.iium.edu.my/14382/ http://irep.iium.edu.my/14382/1/ICMAE%2710_NG_SF.pdf |
| _version_ | 1848777687907172352 |
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| author | Ganikhodjaev, Nasir Zakaria, Siti Fatimah |
| author_facet | Ganikhodjaev, Nasir Zakaria, Siti Fatimah |
| author_sort | Ganikhodjaev, Nasir |
| building | IIUM Repository |
| collection | Online Access |
| description | We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jp and one-level next-nearest neighbour interactions J0. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1 and prolonged next-nearest neighbour interactions Jp contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo … 0. For given lattice model on a Cayley tree, i.e., Jp … 0; Jo … 0 with J1 = 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1 and show that the class of modulated phases consists of socalled antiphase with period 4 only |
| first_indexed | 2025-11-14T14:49:57Z |
| format | Book Chapter |
| id | iium-14382 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:49:57Z |
| publishDate | 2010 |
| publisher | Faculty of Engineering, International Islamic University Malaysia (IIUM) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-143822019-11-20T08:05:09Z http://irep.iium.edu.my/14382/ Phase diagram of the Ising model with next-nearest-neighbour interactions Ganikhodjaev, Nasir Zakaria, Siti Fatimah QA Mathematics We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jp and one-level next-nearest neighbour interactions J0. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1 and prolonged next-nearest neighbour interactions Jp contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo … 0. For given lattice model on a Cayley tree, i.e., Jp … 0; Jo … 0 with J1 = 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1 and show that the class of modulated phases consists of socalled antiphase with period 4 only Faculty of Engineering, International Islamic University Malaysia (IIUM) 2010-08-03 Book Chapter PeerReviewed application/pdf en http://irep.iium.edu.my/14382/1/ICMAE%2710_NG_SF.pdf Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2010) Phase diagram of the Ising model with next-nearest-neighbour interactions. In: Proceedings of International Conference on Mathematical Applications in Engineering. Faculty of Engineering, International Islamic University Malaysia (IIUM), Kuala Lumpur, pp. 355-359. ISBN 9789834309046 |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Zakaria, Siti Fatimah Phase diagram of the Ising model with next-nearest-neighbour interactions |
| title | Phase diagram of the Ising model with next-nearest-neighbour interactions |
| title_full | Phase diagram of the Ising model with next-nearest-neighbour interactions |
| title_fullStr | Phase diagram of the Ising model with next-nearest-neighbour interactions |
| title_full_unstemmed | Phase diagram of the Ising model with next-nearest-neighbour interactions |
| title_short | Phase diagram of the Ising model with next-nearest-neighbour interactions |
| title_sort | phase diagram of the ising model with next-nearest-neighbour interactions |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/14382/ http://irep.iium.edu.my/14382/1/ICMAE%2710_NG_SF.pdf |