Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions
We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jpand one-level next-nearest neighbour interactions J. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1and prolonged next-nearest nei...
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| Format: | Proceeding Paper |
| Language: | English |
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2011
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| Online Access: | http://irep.iium.edu.my/7278/ http://irep.iium.edu.my/7278/2/LIMIT_BEHAVIOR_OF_DYNAMIC_SYSTEMS_CORRESPONDING_TO_LATTICE_MODELS_WITH_COMPETING_PROLONGED_AND_ONE-LEVEL_BINARY_INTERACTIONS.pdf |
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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 Jpand one-level next-nearest neighbour interactions J. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1and prolonged next-nearest neighbour interactions Jpcontains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with J ≠ 0. For given lattice model on a Cayley tree, i.e., Jp≠ 0; J ≠ 0 with J1= 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1and show that the class of modulated phases consists of so-called antiphase with period 4 only. |
| first_indexed | 2025-11-14T14:36:05Z |
| format | Proceeding Paper |
| id | iium-7278 |
| institution | International Islamic University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T14:36:05Z |
| publishDate | 2011 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | iium-72782019-11-20T08:04:08Z http://irep.iium.edu.my/7278/ Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary 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 Jpand one-level next-nearest neighbour interactions J. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1and prolonged next-nearest neighbour interactions Jpcontains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with J ≠ 0. For given lattice model on a Cayley tree, i.e., Jp≠ 0; J ≠ 0 with J1= 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1and show that the class of modulated phases consists of so-called antiphase with period 4 only. 2011-01 Proceeding Paper NonPeerReviewed application/pdf en http://irep.iium.edu.my/7278/2/LIMIT_BEHAVIOR_OF_DYNAMIC_SYSTEMS_CORRESPONDING_TO_LATTICE_MODELS_WITH_COMPETING_PROLONGED_AND_ONE-LEVEL_BINARY_INTERACTIONS.pdf Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2011) Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions. In: IIUM Research, Invention and Innovation Exhibition (IRIIE) 2011, 9-10 February 2011, Cultural Activity Centre (CAC) and KAED Gallery IIUM. (Unpublished) http://www.iium.edu.my/irie/11/ |
| spellingShingle | QA Mathematics Ganikhodjaev, Nasir Zakaria, Siti Fatimah Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions |
| title | Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions |
| title_full | Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions |
| title_fullStr | Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions |
| title_full_unstemmed | Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions |
| title_short | Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions |
| title_sort | limit behavior of dynamic systems corresponding to lattice models with competing prolonged and one-level binary interactions |
| topic | QA Mathematics |
| url | http://irep.iium.edu.my/7278/ http://irep.iium.edu.my/7278/ http://irep.iium.edu.my/7278/2/LIMIT_BEHAVIOR_OF_DYNAMIC_SYSTEMS_CORRESPONDING_TO_LATTICE_MODELS_WITH_COMPETING_PROLONGED_AND_ONE-LEVEL_BINARY_INTERACTIONS.pdf |