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

• Main Authors: Ganikhodjaev, Nasir, Nawi, Ashraf Mohamed
• Format: Article
• Language: English
• Published: American Institute of Physics 2013
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/30049/1/APC001300.pdf; http://irep.iium.edu.my/30049/

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.