On phase diagram of ising model on the cayley tree with restricted competing interactions up to the third-nearest-neighbor generation

Ganikhodjaev, Nasir and Mohd Rodzhan, Mohd Hirzie (2016) On phase diagram of ising model on the cayley tree with restricted competing interactions up to the third-nearest-neighbor generation. In: The 3 rd International Conference on Mathematical Applications in Engineering 2014 (ICMAE’14), 23-25 September, 2014, Sunway Putra Hotel Kuala Lumpur.

	PDF - Published Version Restricted to Repository staff only Download (1MB) | Request a copy
	PDF (SCOPUS) - Published Version Restricted to Repository staff only Download (68kB) | Request a copy
Preview	PDF (WOS) - Supplemental Material Download (130kB) | Preview

Abstract

We study the phase diagram of the Ising model on Cayley tree with competing the first-, second-, and third-nearest-neighbor interactions. We generalize the approach used by Vannimenus for the Ising model with only first- and second- nearest neignbor interactions. The extension of the anisotropic next-nearest-neighbor Ising (ANNNI) model to include third-nearest-neighbor interactions (A3NNI model) has been proposed by Yamada and Hamaya in an attempt to explain the phase diagram structure of several ferroelectric systems of the type A2BX4. We show that the inclusion of the third-nearest-neighbor interactions is essential for the presence of a periodic +++- - - antiphase <3>. In addition, we discuss similarity, in comparison with the phase diagram of the Vannimenus’s approach with competing first- and second-nearest-neighbors. Finally, in the modulated phase was studied in detail where narrow commensurate steps between incommensurate regions appeared when investigating the Lyapunov exponent associated with trajectory of the system

Item Type:	Conference or Workshop Item (Invited Papers)
Additional Information:	4430/50619
Uncontrolled Keywords:	Ising Model, Cayley Tree, Nearest-Neighbor Interactions, Phase Diagram, Modulated Phases
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:	Prof. Nasir Ganikhodjaev
Date Deposited:	13 Jun 2016 15:56
Last Modified:	16 Oct 2017 14:56
URI:	http://irep.iium.edu.my/id/eprint/50619

Actions (login required)

View Item