Potts model with competing interaction up to the third nearest-neighbour generation on a Cayley tree

Potts model with competing interaction up to the third nearest-neighbour generation on a Cayley tree

It is in our interest to investigate the effect of the third nearest-neighbour binary interaction to the phase diagrams of the Potts model on a Cayley tree. Therefore, we generate and analyse the phase diagrams of the Potts model, considering prolonged competing binary interaction J2 and J3 on th...

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Main Authors: Ganikhodjaev, Nasir, Rodzhan, Mohd Hirzie, Basirudin, Sahira
Format: Article
Language:English
English
Published: Malaysian Institute of Physics 2019
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/76974/
http://irep.iium.edu.my/76974/
http://irep.iium.edu.my/76974/1/JFM%20Vol.40%2C%202019.pdf
http://irep.iium.edu.my/76974/7/76974_Potts%20Model%20with%20Competing%20Interaction_wos.pdf
id iium-76974
recordtype eprints
spelling iium-769742020-03-05T08:18:59Z http://irep.iium.edu.my/76974/ Potts model with competing interaction up to the third nearest-neighbour generation on a Cayley tree Ganikhodjaev, Nasir Rodzhan, Mohd Hirzie Basirudin, Sahira QA Mathematics It is in our interest to investigate the effect of the third nearest-neighbour binary interaction to the phase diagrams of the Potts model on a Cayley tree. Therefore, we generate and analyse the phase diagrams of the Potts model, considering prolonged competing binary interaction J2 and J3 on the same branch of the Cayley tree up to the third nearest-neighbour generations. We derive the recurrence system of equations while taking into account some ranges of competing parameters. We carry out a numerical procedure by applying several stability conditions and characteristic points into the iteration scheme. For some non-zero parameter J3, we found the additional phases of period 5, 6, 9, and 11, with the ferromagnetic, antiphase, paramagnetic, antiferromagnetic and modulated phase. For the modulated phase, we further study the existence of phases with period larger than 12 by conducting a numerical analysis on the variation of wavevector and Lyapunov exponent. Malaysian Institute of Physics 2019 Article PeerReviewed application/pdf en http://irep.iium.edu.my/76974/1/JFM%20Vol.40%2C%202019.pdf application/pdf en http://irep.iium.edu.my/76974/7/76974_Potts%20Model%20with%20Competing%20Interaction_wos.pdf Ganikhodjaev, Nasir and Rodzhan, Mohd Hirzie and Basirudin, Sahira (2019) Potts model with competing interaction up to the third nearest-neighbour generation on a Cayley tree. Jurnal Fizik Malaysia, 40 (1). pp. 10008-10021. E-ISSN 2590-4191 http://ifm.org.my/sites/default/files/publications/jfm2019_Vol40No1_10008_0.pdf
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
English
topic QA Mathematics
spellingShingle QA Mathematics
Ganikhodjaev, Nasir
Rodzhan, Mohd Hirzie
Basirudin, Sahira
Potts model with competing interaction up to the third nearest-neighbour generation on a Cayley tree
description It is in our interest to investigate the effect of the third nearest-neighbour binary interaction to the phase diagrams of the Potts model on a Cayley tree. Therefore, we generate and analyse the phase diagrams of the Potts model, considering prolonged competing binary interaction J2 and J3 on the same branch of the Cayley tree up to the third nearest-neighbour generations. We derive the recurrence system of equations while taking into account some ranges of competing parameters. We carry out a numerical procedure by applying several stability conditions and characteristic points into the iteration scheme. For some non-zero parameter J3, we found the additional phases of period 5, 6, 9, and 11, with the ferromagnetic, antiphase, paramagnetic, antiferromagnetic and modulated phase. For the modulated phase, we further study the existence of phases with period larger than 12 by conducting a numerical analysis on the variation of wavevector and Lyapunov exponent.
format Article
author Ganikhodjaev, Nasir
Rodzhan, Mohd Hirzie
Basirudin, Sahira
author_facet Ganikhodjaev, Nasir
Rodzhan, Mohd Hirzie
Basirudin, Sahira
author_sort Ganikhodjaev, Nasir
title Potts model with competing interaction up to the third nearest-neighbour generation on a Cayley tree
title_short Potts model with competing interaction up to the third nearest-neighbour generation on a Cayley tree
title_full Potts model with competing interaction up to the third nearest-neighbour generation on a Cayley tree
title_fullStr Potts model with competing interaction up to the third nearest-neighbour generation on a Cayley tree
title_full_unstemmed Potts model with competing interaction up to the third nearest-neighbour generation on a Cayley tree
title_sort potts model with competing interaction up to the third nearest-neighbour generation on a cayley tree
publisher Malaysian Institute of Physics
publishDate 2019
url http://irep.iium.edu.my/76974/
http://irep.iium.edu.my/76974/
http://irep.iium.edu.my/76974/1/JFM%20Vol.40%2C%202019.pdf
http://irep.iium.edu.my/76974/7/76974_Potts%20Model%20with%20Competing%20Interaction_wos.pdf
first_indexed 2023-09-18T21:48:40Z
last_indexed 2023-09-18T21:48:40Z
_version_ 1777413621663399936

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