Ising model on a general Cayley tree with competing next-nearest-neighbour interactions
We study the Ising model on a general Cayley tree of arbitrary order and produce the phase diagram with competing interactions prolonged next-nearest-neighbour Jp and one-level k-tuple next-nearest-neighbour Jo . Vannimenus proved the existence of modulated phase in the phase diagram of Ising model...
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| Format: | Proceeding Paper |
| Language: | English |
| Published: |
2011
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| Online Access: | http://irep.iium.edu.my/1716/ http://irep.iium.edu.my/1716/2/Ising_Model_on_a_General_Cayley_Tree_with_Competing_Next-nearest-neighbour_Interactions.pdf |
| _version_ | 1848775903176294400 |
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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 Ising model on a general Cayley tree of arbitrary order and produce the phase diagram with competing interactions prolonged next-nearest-neighbour Jp and one-level k-tuple next-nearest-neighbour Jo . Vannimenus proved the existence of modulated phase in the phase diagram of Ising model with competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interactions Jp, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo ≠ 0. For a given lattice model on a Cayley tree, i.e., Jp ≠ 0; Jo ≠ 0 with J1 = 0, we describe the general equation, phase diagram and clarify the role of nearest-neighbour interaction J1. In the presence of nearest-neighbour interaction J1, Vannimenus demonstrated that for arbitrary random initial data one can reach the same phase diagram. We show that in the case J1 = 0 the set of all possible initial data can reach different phase diagrams |
| first_indexed | 2025-11-14T14:21:35Z |
| format | Proceeding Paper |
| id | iium-1716 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:21:35Z |
| publishDate | 2011 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-17162019-11-20T08:03:27Z http://irep.iium.edu.my/1716/ Ising model on a general Cayley tree with competing next-nearest-neighbour interactions Ganikhodjaev, Nasir Zakaria, Siti Fatimah QA Mathematics QC Physics We study the Ising model on a general Cayley tree of arbitrary order and produce the phase diagram with competing interactions prolonged next-nearest-neighbour Jp and one-level k-tuple next-nearest-neighbour Jo . Vannimenus proved the existence of modulated phase in the phase diagram of Ising model with competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interactions Jp, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo ≠ 0. For a given lattice model on a Cayley tree, i.e., Jp ≠ 0; Jo ≠ 0 with J1 = 0, we describe the general equation, phase diagram and clarify the role of nearest-neighbour interaction J1. In the presence of nearest-neighbour interaction J1, Vannimenus demonstrated that for arbitrary random initial data one can reach the same phase diagram. We show that in the case J1 = 0 the set of all possible initial data can reach different phase diagrams 2011-04 Proceeding Paper PeerReviewed application/pdf en http://irep.iium.edu.my/1716/2/Ising_Model_on_a_General_Cayley_Tree_with_Competing_Next-nearest-neighbour_Interactions.pdf Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2011) Ising model on a general Cayley tree with competing next-nearest-neighbour interactions. In: Annual International Conference on Operations Research and Statistics, 7-8 April 2011, Penang, Malaysia. http://dl.globalstf.org/index.php?page=shop.product_details&flypage=flypage_images.tpl&product_id=624&category_id=47&option=com_virtuemart&Itemid=4 |
| spellingShingle | QA Mathematics QC Physics Ganikhodjaev, Nasir Zakaria, Siti Fatimah Ising model on a general Cayley tree with competing next-nearest-neighbour interactions |
| title | Ising model on a general Cayley tree with competing next-nearest-neighbour interactions |
| title_full | Ising model on a general Cayley tree with competing next-nearest-neighbour interactions |
| title_fullStr | Ising model on a general Cayley tree with competing next-nearest-neighbour interactions |
| title_full_unstemmed | Ising model on a general Cayley tree with competing next-nearest-neighbour interactions |
| title_short | Ising model on a general Cayley tree with competing next-nearest-neighbour interactions |
| title_sort | ising model on a general cayley tree with competing next-nearest-neighbour interactions |
| topic | QA Mathematics QC Physics |
| url | http://irep.iium.edu.my/1716/ http://irep.iium.edu.my/1716/ http://irep.iium.edu.my/1716/2/Ising_Model_on_a_General_Cayley_Tree_with_Competing_Next-nearest-neighbour_Interactions.pdf |