Attractors on Ising Model with Restricted Interactions on Cayley Tree of Order 2
We consider an Ising model on a Cayley tree with competing interactions of the next-nearest-neighbours of two types: prolonged and one-level interactions only. More recently, Ganikhodjaev and Zakaria investigated the same model and proved that its phase diagram contain only four phases, namely, ferr...
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American Institute of Physics
2013
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| Online Access: | http://irep.iium.edu.my/30049/ http://irep.iium.edu.my/30049/ http://irep.iium.edu.my/30049/1/APC001300.pdf |
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iium-300492013-07-24T07:39:57Z http://irep.iium.edu.my/30049/ Attractors on Ising Model with Restricted Interactions on Cayley Tree of Order 2 Ganikhodjaev, Nasir Nawi, Ashraf Mohamed QA Mathematics We consider an Ising model on a Cayley tree with competing interactions of the next-nearest-neighbours of two types: prolonged and one-level interactions only. More recently, Ganikhodjaev and Zakaria investigated the same model and proved that its phase diagram contain only four phases, namely, ferromagnetic, paramagnetic, antiferromagnetic and antiphase. In this paper we reinvestigate the phase diagram of this model using an iterative scheme, that is developed for a renormalized effective nearest-neighbour coupling Kr and effective field per site Xr for spins on the n-th level of a Cayley tree with competing one-level J0 and prolonged Jp next-nearest-neighbour interactions between Ising spins on the tree. We find an intermediate range of Jp/J0 values where Xr and Kr iterate to a finite attractor in the X - K plane. American Institute of Physics 2013-04 Article PeerReviewed application/pdf en http://irep.iium.edu.my/30049/1/APC001300.pdf Ganikhodjaev, Nasir and Nawi, Ashraf Mohamed (2013) Attractors on Ising Model with Restricted Interactions on Cayley Tree of Order 2. AIP Conference Proceedings , 1522. pp. 1300-1305. ISSN 0094-243X (P), 1551-7616 (O) 10.1063/1.4801280 |
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Local University |
| institution |
International Islamic University Malaysia |
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Online Access |
| language |
English |
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QA Mathematics |
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QA Mathematics Ganikhodjaev, Nasir Nawi, Ashraf Mohamed Attractors on Ising Model with Restricted Interactions on Cayley Tree of Order 2 |
| description |
We consider an Ising model on a Cayley tree with competing interactions of the next-nearest-neighbours of two types: prolonged and one-level interactions only. More recently, Ganikhodjaev and Zakaria investigated the same model and proved that its phase diagram contain only four phases, namely, ferromagnetic, paramagnetic, antiferromagnetic and antiphase. In this paper we reinvestigate the phase diagram of this model using an iterative scheme, that is developed for a renormalized effective nearest-neighbour coupling Kr and effective field per site Xr for spins on the n-th level of a Cayley tree with competing one-level J0 and prolonged Jp next-nearest-neighbour interactions between Ising spins on the tree. We find an intermediate range of Jp/J0 values where Xr and Kr iterate to a finite attractor in the X - K plane. |
| format |
Article |
| author |
Ganikhodjaev, Nasir Nawi, Ashraf Mohamed |
| author_facet |
Ganikhodjaev, Nasir Nawi, Ashraf Mohamed |
| author_sort |
Ganikhodjaev, Nasir |
| title |
Attractors on Ising Model with Restricted Interactions on
Cayley Tree of Order 2 |
| title_short |
Attractors on Ising Model with Restricted Interactions on
Cayley Tree of Order 2 |
| title_full |
Attractors on Ising Model with Restricted Interactions on
Cayley Tree of Order 2 |
| title_fullStr |
Attractors on Ising Model with Restricted Interactions on
Cayley Tree of Order 2 |
| title_full_unstemmed |
Attractors on Ising Model with Restricted Interactions on
Cayley Tree of Order 2 |
| title_sort |
attractors on ising model with restricted interactions on
cayley tree of order 2 |
| publisher |
American Institute of Physics |
| publishDate |
2013 |
| url |
http://irep.iium.edu.my/30049/ http://irep.iium.edu.my/30049/ http://irep.iium.edu.my/30049/1/APC001300.pdf |
| first_indexed |
2023-09-18T20:44:07Z |
| last_indexed |
2023-09-18T20:44:07Z |
| _version_ |
1777409560305205248 |