Phase diagram of the Ising model 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: | Proceeding Paper |
| Language: | English |
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2010
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| Online Access: | http://irep.iium.edu.my/1743/ http://irep.iium.edu.my/1743/2/ICMAE2010-SITI_FATIMAH.pdf |
| _version_ | 1848775908559683584 |
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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 so-called antiphase with period 4 only.
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| first_indexed | 2025-11-14T14:21:40Z |
| format | Proceeding Paper |
| id | iium-1743 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:40Z |
| publishDate | 2010 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-17432019-11-20T08:04:39Z http://irep.iium.edu.my/1743/ Phase diagram of the Ising model next-nearest-neighbour interactions Ganikhodjaev, Nasir Zakaria, Siti Fatimah QA Mathematics QC Physics 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 so-called antiphase with period 4 only. 2010-08 Proceeding Paper NonPeerReviewed application/pdf en http://irep.iium.edu.my/1743/2/ICMAE2010-SITI_FATIMAH.pdf Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2010) Phase diagram of the Ising model next-nearest-neighbour interactions. In: International Conference on Mathematical Applications in Engineering (ICMAE’10), 3 - 4 Aug, 2010, Kuala Lumpur. |
| spellingShingle | QA Mathematics QC Physics Ganikhodjaev, Nasir Zakaria, Siti Fatimah Phase diagram of the Ising model next-nearest-neighbour interactions |
| title | Phase diagram of the Ising model next-nearest-neighbour interactions |
| title_full | Phase diagram of the Ising model next-nearest-neighbour interactions |
| title_fullStr | Phase diagram of the Ising model next-nearest-neighbour interactions |
| title_full_unstemmed | Phase diagram of the Ising model next-nearest-neighbour interactions |
| title_short | Phase diagram of the Ising model next-nearest-neighbour interactions |
| title_sort | phase diagram of the ising model next-nearest-neighbour interactions |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/1743/ http://irep.iium.edu.my/1743/2/ICMAE2010-SITI_FATIMAH.pdf |