LYAPUNOV EXPONENTS AND MODULATED PHASES OF AN ISING MODEL ON CAYLEY TREE OF ARBITRARY ORDER

Selman Uguz (), Nasir Ganikhodjaev (), Hasan Akin () and Seyit Temir ()
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Selman Uguz: Department of Mathematics, Arts and Science Faculty Harran University, Sanliurfa, 63200, Turkey
Nasir Ganikhodjaev: Department of Computational and Theoretical Sciences, Faculty of Science, IIUM, 25200 Kuantan, Malaysia
Hasan Akin: Department of Mathematics, Faculty of Education, Zirve University, 27260, Gaziantep, Turkey
Seyit Temir: Department of Mathematics, Arts and Science Faculty Harran University, Sanliurfa, 63200, Turkey

International Journal of Modern Physics C (IJMPC), 2012, vol. 23, issue 05, 1-15

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 interactionJ1, prolonged next-nearest-neighbor interactionJpand ternary prolonged interactionJtpis considered on a Cayley tree of arbitrary orderk. 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 ofα = T/J1,β = −Jp/J1andγ = -Jtp/J1. This study recovers as particular cases, previous work by Vannimenus1withγ = 0fork = 2and Ganikhodjaevet al.2in the presenceJ1,Jp,Jtpwithk = 2. The variation of the wavevectorqwith temperature in the modulated phase and the Lyapunov exponent associated with the trajectory of our iterative system are studied in detail.

Keywords: Ising model; Cayley tree; phase diagram; next-nearest-neighbor interactions; modulated phase; Lyapunov exponent; 05.50.+q; 64.60.-i; 64.60.De; 75.10.Hk (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183112500398

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