Ising model with restricted interactions on general Cayley tree of arbitrary order

Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2011) Ising model with restricted interactions on general Cayley tree of arbitrary order. Australian Journal of Basic and Applied Sciences, 5 (8). pp. 1296-1304. ISSN 1991-8178

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Abstract

We study an Ising model on a general Cayley tree with competing interaction of next-nearest-neighbour of two types; prolonged and one-level k-tuple interactions. Vannimenus covers a study of Ising model on competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interaction Jp. Later Mariz et al extend Vannimenus work by adding a one-level interaction Jo for order 2 with the existence of external magnetic field. And recently Ganikhodjaev et al found only simple modulated phases exist for Ising model with second neighbour prolonged and one-level competing interaction of order 2. So, in this paper, we study the Ising model with competing interaction J0≠0, Jp≠0 and J1=0 to identify the preservation of those phases for higher order k. We derived two types of general system of equations and describe the phase diagram for both cases of even and odd order.

Item Type:	Article (Journal)
Additional Information:	4430/7134
Uncontrolled Keywords:	Ising models, Cayley tree, prolonged next-nearest-neighbour, one-level nextnearest-neighbour.
Subjects:	Q Science > QA Mathematics Q Science > QC Physics
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:	18 Nov 2011 12:59
Last Modified:	20 Nov 2019 16:07
URI:	http://irep.iium.edu.my/id/eprint/7134

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