Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions

Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2011) Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions. In: IIUM Research, Invention and Innovation Exhibition (IRIIE) 2011, 9-10 February 2011, Cultural Activity Centre (CAC) and KAED Gallery IIUM. (Unpublished)

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Abstract

We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jpand one-level next-nearest neighbour interactions J. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1and prolonged next-nearest neighbour interactions Jpcontains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with J ≠ 0. For given lattice model on a Cayley tree, i.e., Jp≠ 0; J ≠ 0 with J1= 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1and show that the class of modulated phases consists of so-called antiphase with period 4 only.

Item Type:	Conference or Workshop Item (Poster)
Additional Information:	4430/7278
Uncontrolled Keywords:	Lattice models, Cayley tree, prolonged next-nearest neighbour, one-level next-nearest neighbour, modulated phase.
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 Dec 2011 10:03
Last Modified:	20 Nov 2019 16:04
URI:	http://irep.iium.edu.my/id/eprint/7278

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