Strange attractors in the Vannimenus model on an arbitrary order cayley tree

Ganikhodjaev, Nasir and Akin, Hasan and Temir, Seyit and Uguz, Selman and Nawi, Ashraf Mohamed (2013) Strange attractors in the Vannimenus model on an arbitrary order cayley tree. Journal of Physics: Conference Series, 435 (012031). 012031-1. ISSN 1742-6588 (P), 1742-6596 (O)

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Abstract

We consider the Vannimenus model on a Cayley tree of arbitrary order k with competing nearest-neighbour interactions J1 and next-nearest-neighbour interactions J2 and J3 in the presence of an external magnetic field h. In this paper we study the phase diagram of the model using an iterative scheme for a renormalized effective nearest-neighbour coupling Kr and effective field per site Xr for spins on the rth level; it recovers, as particular cases, previous works by Vannimenus, Inawashiro et al, Mariz et al and Ganikhodjaev and Uǧuz. Each phase is characterized by a particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into few disconnected pieces, etc) are exhibited for typical values of parameters.

Item Type:	Article (Journal)
Additional Information:	4430/30026
Uncontrolled Keywords:	Condensed matter: electrical, magnetic and optical
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:	05 Aug 2013 09:47
Last Modified:	05 Aug 2013 09:47
URI:	http://irep.iium.edu.my/id/eprint/30026

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