Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order

Uguz, Selman and Ganikhodjaev, Nasir and Akin, Hasan and Temir, Seyit (2012) Lyapunov exponents and modulated phases of an ising model on cayley tree of arbitrary order. International Journal of Modern Physics C, 23 (5). 1250039 (1)-1250039 (15). ISSN 1793-6586 (O), 0129-1831 (P)

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Abstract

Different types of the lattice spin systems with the competing interactions have rich and interesting phase diagrams. In this study a system with competing nearest-neighbor interaction J1, prolonged next-nearest-neighbor interaction Jp and ternary prolonged interaction Jtp is considered on a Cayley tree of arbitrary order k. To perform this study, an iterative scheme is developed for the corresponding Hamiltonian model. At finite temperatures several interesting properties are presented for typical values of α = T/J1, β = −Jp/J1 and γ = -Jtp/J1. This study recovers as particular cases, previous work by Vannimenus1 with γ = 0 for k = 2 and Ganikhodjaev et al.2 in the presence J1, Jp, Jtp with k = 2. The variation of the wavevector q with temperature in the modulated phase and the Lyapunov exponent associated with the trajectory of our iterative system are studied in detail.

Item Type:	Article (Journal)
Additional Information:	4430/24304
Uncontrolled Keywords:	Ising model; Cayley tree; phase diagram; next-nearest-neighbor interactions; modulated phase; Lyapunov exponent
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:	11 Jun 2012 09:49
Last Modified:	11 Jun 2012 09:49
URI:	http://irep.iium.edu.my/id/eprint/24304

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