Ising model with competing interactions on Cayley tree of Order 4: an analytic solution

Ali, Rukiah and Mukhamedov, Farrukh and Pah, Chin Hee (2013) Ising model with competing interactions on Cayley tree of Order 4: an analytic solution. Journal of Physics: Conference Series, 435. 012032. ISSN 1742-6588 (P), 1742-6596 (O)

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Abstract

We investigate an Ising model with two restricted competing interactions (nearest neighbors, and one-level neighbors) on the Cayley tree of order four. We derive a recurrent equation for the Cayley tree of order k. We found an analytic solution for the given interactions in the case of order 4. Our result of the critical curve shows the existence of the phase transition occurs in this model. We also give the calculation of the free energy from the description of Gibbs measure of the given Hamiltonian on Cayley tree of order four.

Item Type:	Article (Journal)
Additional Information:	5537/30083
Uncontrolled Keywords:	Analytic solution; Cayley trees; Competing interactions; Critical curve; Gibbs measure; Nearest neighbors; Recurrent equations
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:	Dr. Farrukh Mukhamedov
Date Deposited:	13 Jun 2013 13:17
Last Modified:	24 Jul 2013 12:48
URI:	http://irep.iium.edu.my/id/eprint/30083

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