Attractors on Ising Model with Restricted Interactions on Cayley Tree of Order 2

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)

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	4430/30049
Uncontrolled Keywords:	Ising model, Cayley tree, next-nearest-neighbour, attractor
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Prof. Nasir Ganikhodjaev
Date Deposited:	24 Jul 2013 15:39
Last Modified:	24 Jul 2013 15:39
URI:	http://irep.iium.edu.my/id/eprint/30049

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