Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree

Ganikhodjaev, Nasir and Akin, Hasan and Uguz, Selman and Temir, Seyit (2011) Phase diagrams of an Ising system with competing binary, prolonged ternary and next-nearest interactions on a Cayley tree. Journal of Concrete and Applicable Mathematics, 9 (1). pp. 26-34. ISSN 1559-176X (O), 1548-5390 (P)

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Abstract

In this paper we consider the Ising model with spin values in Φ = {−1, 1}, the relevant Hamiltonian with competing binary nearest-neighbor, prolonged ternary and prolonged next-nearest neighbors interactions has the form H(σ) = −Jp �� >x,y< σ(x)σ(y) − Jt >x�,¯y,z< σ(x)σ(y)σ(z)− J1 � <x,y>σ(x)σ(y), where Jp, Jt, J1 ∈ R are coupling constants. We study the phase diagram of this model. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established. At vanishing temperature, the phase diagram is fully determined for all values and signs of J1, Jt and Jp. At finite temperatures several interesting features are exhibited for typical values of −Jt/J1 and Jp/J1.

Item Type:	Article (Journal)
Additional Information:	4430/1688
Uncontrolled Keywords:	Ising model, Cayley tree, phase diagram, ternary neighbors, modulated phase, Lifshitz point.
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:	22 Nov 2011 14:29
Last Modified:	13 Dec 2011 16:45
URI:	http://irep.iium.edu.my/id/eprint/1688

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