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

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

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 nex...

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Main Authors: Ganikhodjaev, Nasir, Mohd Rodzhan, Mohd Hirzie
Format: Conference or Workshop Item
Language:English
English
English
Published: Institute for Mathematical Research 2016
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/50619/
http://irep.iium.edu.my/50619/
http://irep.iium.edu.my/50619/1/50619_On%20phase%20diagram_complete.pdf
http://irep.iium.edu.my/50619/2/50619_On%20phase%20diagram_SCOPUS.pdf
http://irep.iium.edu.my/50619/13/50619_On%20phase%20diagram_WOS.pdf
id iium-50619
recordtype eprints
spelling iium-506192017-10-16T06:56:11Z http://irep.iium.edu.my/50619/ On phase diagram of ising model on the cayley tree with restricted competing interactions up to the third-nearest-neighbor generation Ganikhodjaev, Nasir Mohd Rodzhan, Mohd Hirzie QA Mathematics 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 Institute for Mathematical Research 2016-02 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/50619/1/50619_On%20phase%20diagram_complete.pdf application/pdf en http://irep.iium.edu.my/50619/2/50619_On%20phase%20diagram_SCOPUS.pdf application/pdf en http://irep.iium.edu.my/50619/13/50619_On%20phase%20diagram_WOS.pdf 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. http://einspem.upm.edu.my/journal/
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
English
English
topic QA Mathematics
spellingShingle QA Mathematics
Ganikhodjaev, Nasir
Mohd Rodzhan, Mohd Hirzie
On phase diagram of ising model on the cayley tree with restricted competing interactions up to the third-nearest-neighbor generation
description 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
format Conference or Workshop Item
author Ganikhodjaev, Nasir
Mohd Rodzhan, Mohd Hirzie
author_facet Ganikhodjaev, Nasir
Mohd Rodzhan, Mohd Hirzie
author_sort Ganikhodjaev, Nasir
title On phase diagram of ising model on the cayley tree with restricted competing interactions up to the third-nearest-neighbor generation
title_short On phase diagram of ising model on the cayley tree with restricted competing interactions up to the third-nearest-neighbor generation
title_full On phase diagram of ising model on the cayley tree with restricted competing interactions up to the third-nearest-neighbor generation
title_fullStr On phase diagram of ising model on the cayley tree with restricted competing interactions up to the third-nearest-neighbor generation
title_full_unstemmed On phase diagram of ising model on the cayley tree with restricted competing interactions up to the third-nearest-neighbor generation
title_sort on phase diagram of ising model on the cayley tree with restricted competing interactions up to the third-nearest-neighbor generation
publisher Institute for Mathematical Research
publishDate 2016
url http://irep.iium.edu.my/50619/
http://irep.iium.edu.my/50619/
http://irep.iium.edu.my/50619/1/50619_On%20phase%20diagram_complete.pdf
http://irep.iium.edu.my/50619/2/50619_On%20phase%20diagram_SCOPUS.pdf
http://irep.iium.edu.my/50619/13/50619_On%20phase%20diagram_WOS.pdf
first_indexed 2023-09-18T21:11:33Z
last_indexed 2023-09-18T21:11:33Z
_version_ 1777411286326312960

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