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Phase diagram of the Ising model next-nearest-neighbour interactions

Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2010) Phase diagram of the Ising model next-nearest-neighbour interactions. In: International Conference on Mathematical Applications in Engineering (ICMAE’10), 3 - 4 Aug, 2010, Kuala Lumpur.

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Abstract

We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jp and one-level next-nearest neighbour interactions J0. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1 and prolonged next-nearest neighbour interactions Jp contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo ≠ 0. For given lattice model on a Cayley tree, i.e., Jp ≠ 0; Jo ≠ 0 with J1 = 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1 and show that the class of modulated phases consists of so-called antiphase with period 4 only.

Item Type: Conference or Workshop Item (Full Paper)
Additional Information: 4430/1743
Uncontrolled Keywords: Lattice models, Cayley tree, prolonged next-nearest neighbour, one-level next-nearest neighbour, modulated phase.
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: 30 Nov 2011 14:52
Last Modified: 30 Nov 2011 17:11
URI: http://irep.iium.edu.my/id/eprint/1743

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