Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions

We study the phase diagram for Potts model on a Cayley tree with competing nearestneighbor interactions J1, prolonged next-nearest-neighbor interactions J2 and one-level nextnearest- neighbor interactions J3. Vannimenus [1] proved that the phase diagram of Ising model with Jo = 0 contains a modulate...

Full description

Bibliographic Details
Main Author:	Ganikhodjaev, Nasir
Format:	Conference or Workshop Item
Language:	English
Published:	EUDOXUS PRESS, LLC 2010
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/1689/ http://irep.iium.edu.my/1689/ http://irep.iium.edu.my/1689/1/abstract_CCS_2010.pdf

id	iium-1689
recordtype	eprints
spelling	iium-16892011-12-12T02:55:06Z http://irep.iium.edu.my/1689/ Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions Ganikhodjaev, Nasir QA Mathematics We study the phase diagram for Potts model on a Cayley tree with competing nearestneighbor interactions J1, prolonged next-nearest-neighbor interactions J2 and one-level nextnearest- neighbor interactions J3. Vannimenus [1] proved that the phase diagram of Ising model with Jo = 0 contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al [2] generalized this result for Ising model with Jo 6= 0 and recently anikhodjaev et al [3] proved similar result for the three-state Potts model with Jo = 0. For given lattice model on a Cayley tree we produce recursive relations obtained following the lines of Inawashiro et al [4]. These recursive relations provide us the numerically exact phase diagram of the model. 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 J2/J1, J3/J1. EUDOXUS PRESS, LLC 2010-05-24 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/1689/1/abstract_CCS_2010.pdf Ganikhodjaev, Nasir (2010) Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions. In: 3rd International Interdisciplinary Chaos Symposium on Chaos and Complex Systems, 21-24 May 2010, Istanbul, Turkey. (Unpublished) http://www.iku.edu.tr/TR/semp_icerik.php?p=159&r=0
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 Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions
description	We study the phase diagram for Potts model on a Cayley tree with competing nearestneighbor interactions J1, prolonged next-nearest-neighbor interactions J2 and one-level nextnearest- neighbor interactions J3. Vannimenus [1] proved that the phase diagram of Ising model with Jo = 0 contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al [2] generalized this result for Ising model with Jo 6= 0 and recently anikhodjaev et al [3] proved similar result for the three-state Potts model with Jo = 0. For given lattice model on a Cayley tree we produce recursive relations obtained following the lines of Inawashiro et al [4]. These recursive relations provide us the numerically exact phase diagram of the model. 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 J2/J1, J3/J1.
format	Conference or Workshop Item
author	Ganikhodjaev, Nasir
author_facet	Ganikhodjaev, Nasir
author_sort	Ganikhodjaev, Nasir
title	Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions
title_short	Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions
title_full	Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions
title_fullStr	Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions
title_full_unstemmed	Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions
title_sort	strange attractor in the potts model on a cayley tree in the presence of competing interactions
publisher	EUDOXUS PRESS, LLC
publishDate	2010
url	http://irep.iium.edu.my/1689/ http://irep.iium.edu.my/1689/ http://irep.iium.edu.my/1689/1/abstract_CCS_2010.pdf
first_indexed	2023-09-18T20:09:09Z
last_indexed	2023-09-18T20:09:09Z
_version_	1777407360033095680

Strange attractor in the Potts model on a Cayley tree in the presence of competing interactions

Similar Items