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Ising model on a general Cayley tree with competing next-nearest-neighbour interactions

Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2011) Ising model on a general Cayley tree with competing next-nearest-neighbour interactions. In: Annual International Conference on Operations Research and Statistics, 7-8 April 2011, Penang, Malaysia.

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We study the Ising model on a general Cayley tree of arbitrary order and produce the phase diagram with competing interactions prolonged next-nearest-neighbour Jp and one-level k-tuple next-nearest-neighbour Jo . Vannimenus proved the existence of modulated phase in the phase diagram of Ising model with competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interactions Jp, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo ≠ 0. For a given lattice model on a Cayley tree, i.e., Jp ≠ 0; Jo ≠ 0 with J1 = 0, we describe the general equation, phase diagram and clarify the role of nearest-neighbour interaction J1. In the presence of nearest-neighbour interaction J1, Vannimenus demonstrated that for arbitrary random initial data one can reach the same phase diagram. We show that in the case J1 = 0 the set of all possible initial data can reach different phase diagrams

Item Type: Conference or Workshop Item (UNSPECIFIED)
Additional Information: 4430/1716 (The Conference Proceedings (Print ISSN: 2251-1938, E-Periodical ISSN: 2251-1946, ISBN: 978-981-08-8407-9) will be indexed by EBSCO, CrossRef, Proquest and will be submitted to Scopus, ScienceDirect and amongst others, where applicable
Uncontrolled Keywords: Ising model, Cayley tree, prolonged next-nearest-neighbour, one-level next-nearest-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: 05 Dec 2011 09:07
Last Modified: 20 Nov 2019 16:03
URI: http://irep.iium.edu.my/id/eprint/1716

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