Strange attractors in the Vannimenus model on an arbitrary order cayley tree

Strange attractors in the Vannimenus model on an arbitrary order cayley tree

We consider the Vannimenus model on a Cayley tree of arbitrary order k with competing nearest-neighbour interactions J1 and next-nearest-neighbour interactions J2 and J3 in the presence of an external magnetic field h. In this paper we study the phase diagram of the model using an iterative scheme f...

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Main Authors: Ganikhodjaev, Nasir, Akin, Hasan, Temir, Seyit, Uguz, Selman, Nawi, Ashraf Mohamed
Format: Article
Language:English
Published: Institute of Physics Publishing (UK) 2013
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/30026/
http://irep.iium.edu.my/30026/
http://irep.iium.edu.my/30026/
http://irep.iium.edu.my/30026/1/iCAST2012_Akin_etc.pdf
id iium-30026
recordtype eprints
spelling iium-300262013-08-05T01:47:46Z http://irep.iium.edu.my/30026/ Strange attractors in the Vannimenus model on an arbitrary order cayley tree Ganikhodjaev, Nasir Akin, Hasan Temir, Seyit Uguz, Selman Nawi, Ashraf Mohamed QA Mathematics We consider the Vannimenus model on a Cayley tree of arbitrary order k with competing nearest-neighbour interactions J1 and next-nearest-neighbour interactions J2 and J3 in the presence of an external magnetic field h. In this paper we study the phase diagram of the model using an iterative scheme for a renormalized effective nearest-neighbour coupling Kr and effective field per site Xr for spins on the rth level; it recovers, as particular cases, previous works by Vannimenus, Inawashiro et al, Mariz et al and Ganikhodjaev and Uǧuz. Each phase is characterized by a particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into few disconnected pieces, etc) are exhibited for typical values of parameters. Institute of Physics Publishing (UK) 2013-04 Article PeerReviewed application/pdf en http://irep.iium.edu.my/30026/1/iCAST2012_Akin_etc.pdf Ganikhodjaev, Nasir and Akin, Hasan and Temir, Seyit and Uguz, Selman and Nawi, Ashraf Mohamed (2013) Strange attractors in the Vannimenus model on an arbitrary order cayley tree. Journal of Physics: Conference Series, 435 (012031). 012031-1. ISSN 1742-6588 (P), 1742-6596 (O) http://iopscience.iop.org/1742-6596/435/1/012031 10.1088/1742-6596/435/1/012031
repository_type Digital Repository
institution_category Local University
institution International Islamic University Malaysia
building IIUM Repository
collection Online Access
language English
topic QA Mathematics
spellingShingle QA Mathematics
Ganikhodjaev, Nasir
Akin, Hasan
Temir, Seyit
Uguz, Selman
Nawi, Ashraf Mohamed
Strange attractors in the Vannimenus model on an arbitrary order cayley tree
description We consider the Vannimenus model on a Cayley tree of arbitrary order k with competing nearest-neighbour interactions J1 and next-nearest-neighbour interactions J2 and J3 in the presence of an external magnetic field h. In this paper we study the phase diagram of the model using an iterative scheme for a renormalized effective nearest-neighbour coupling Kr and effective field per site Xr for spins on the rth level; it recovers, as particular cases, previous works by Vannimenus, Inawashiro et al, Mariz et al and Ganikhodjaev and Uǧuz. Each phase is characterized by a particular attractor and the phase diagram is obtained by following the evolution and detecting the qualitative changements of these attractors. These changements can be either continuous or abrupt, respectively characterizing second- or first- order phase transitions. We present a few typical attractors and at finite temperatures, several interesting features (evolution of reentrances, separation of the modulated region into few disconnected pieces, etc) are exhibited for typical values of parameters.
format Article
author Ganikhodjaev, Nasir
Akin, Hasan
Temir, Seyit
Uguz, Selman
Nawi, Ashraf Mohamed
author_facet Ganikhodjaev, Nasir
Akin, Hasan
Temir, Seyit
Uguz, Selman
Nawi, Ashraf Mohamed
author_sort Ganikhodjaev, Nasir
title Strange attractors in the Vannimenus model on an arbitrary order cayley tree
title_short Strange attractors in the Vannimenus model on an arbitrary order cayley tree
title_full Strange attractors in the Vannimenus model on an arbitrary order cayley tree
title_fullStr Strange attractors in the Vannimenus model on an arbitrary order cayley tree
title_full_unstemmed Strange attractors in the Vannimenus model on an arbitrary order cayley tree
title_sort strange attractors in the vannimenus model on an arbitrary order cayley tree
publisher Institute of Physics Publishing (UK)
publishDate 2013
url http://irep.iium.edu.my/30026/
http://irep.iium.edu.my/30026/
http://irep.iium.edu.my/30026/
http://irep.iium.edu.my/30026/1/iCAST2012_Akin_etc.pdf
first_indexed 2023-09-18T20:44:05Z
last_indexed 2023-09-18T20:44:05Z
_version_ 1777409558307667968

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