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Lyapunov Exponents And Modulated Phases Of An Ising Model On Cayley Tree Of Arbitrary Order

Author

Listed:
  • 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)

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.

Suggested Citation

  • Selman Uguz & Nasir Ganikhodjaev & Hasan Akin & Seyit Temir, 2012. "Lyapunov Exponents And Modulated Phases Of An Ising Model On Cayley Tree Of Arbitrary Order," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 23(05), pages 1-15.
    • Handle: RePEc:wsi:ijmpcx:v:23:y:2012:i:05:n:s0129183112500398
    DOI: 10.1142/S0129183112500398
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    Cited by:

    1. Akın, Hasan & Ulusoy, Suleyman, 2023. "A new approach to studying the thermodynamic properties of the q-state Potts model on a Cayley tree," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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