Modulated phase of a Potts Model with competing binary interactions on a Cayley tree

We study the phase diagram for Potts model on a Cayley tree with competing nearest-neighbor interactions J1, prolonged next-nearest-neighbor interactions Jp and one-level next-nearest-neighbor interactions Jo. Vannimenus proved that the phase diagram of Ising model with Jo=0 contains a modulated pha...

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Main Authors:	Ganikhodjaev, Nasir, Temir, Seyit, Akin, Hasan
Format:	Article
Language:	English
Published:	Springer Link 2009
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/1639/ http://irep.iium.edu.my/1639/ http://irep.iium.edu.my/1639/ http://irep.iium.edu.my/1639/1/Modulated-phase-of-a-potts-model-with-competing-binary-interactions-on-a-cayley-tree_2009_Journal-of-Statistical-Physics.pdf

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spelling	iium-16392011-09-05T08:38:59Z http://irep.iium.edu.my/1639/ Modulated phase of a Potts Model with competing binary interactions on a Cayley tree Ganikhodjaev, Nasir Temir, Seyit Akin, Hasan QA Mathematics We study the phase diagram for Potts model on a Cayley tree with competing nearest-neighbor interactions J1, prolonged next-nearest-neighbor interactions Jp and one-level next-nearest-neighbor interactions Jo. Vannimenus proved that the phase diagram of Ising model with Jo=0 contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature. Later Mariz et al. generalized this result for Ising model with Jo≠0 and recently Ganikhodjaev et al. proved similar result for the three-state Potts model with Jo=0. We consider Potts model with Jo≠0 and show that for some values of Jo the multicritical Lifshitz point be at non-zero temperature. We also prove that as soon as the same-level interactionJo is nonzero, the paramagnetic phase found at high temperatures for Jo=0 disappears, while Ising model does not obtain such property. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular case, previous work by Ganikhodjaev et al. for Jo=0. At vanishing temperature, the phase diagram is fully determined for all values and signs of J1,Jp and Jo. At finite temperatures several interesting features are exhibited for typical values of Jo/J1. Springer Link 2009 Article PeerReviewed application/pdf en http://irep.iium.edu.my/1639/1/Modulated-phase-of-a-potts-model-with-competing-binary-interactions-on-a-cayley-tree_2009_Journal-of-Statistical-Physics.pdf Ganikhodjaev, Nasir and Temir, Seyit and Akin, Hasan (2009) Modulated phase of a Potts Model with competing binary interactions on a Cayley tree. Journal of Statistical Physics, 137 (4). pp. 701-715. ISSN 0022-4715 http://www.springerlink.com/content/102588/ 10.1007/s10955-009-9869-z
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 Temir, Seyit Akin, Hasan Modulated phase of a Potts Model with competing binary interactions on a Cayley tree
description	We study the phase diagram for Potts model on a Cayley tree with competing nearest-neighbor interactions J1, prolonged next-nearest-neighbor interactions Jp and one-level next-nearest-neighbor interactions Jo. Vannimenus proved that the phase diagram of Ising model with Jo=0 contains a modulated phase, as found for similar models on periodic lattices, but the multicritical Lifshitz point is at zero temperature. Later Mariz et al. generalized this result for Ising model with Jo≠0 and recently Ganikhodjaev et al. proved similar result for the three-state Potts model with Jo=0. We consider Potts model with Jo≠0 and show that for some values of Jo the multicritical Lifshitz point be at non-zero temperature. We also prove that as soon as the same-level interactionJo is nonzero, the paramagnetic phase found at high temperatures for Jo=0 disappears, while Ising model does not obtain such property. To perform this study, an iterative scheme similar to that appearing in real space renormalization group frameworks is established; it recovers, as particular case, previous work by Ganikhodjaev et al. for Jo=0. At vanishing temperature, the phase diagram is fully determined for all values and signs of J1,Jp and Jo. At finite temperatures several interesting features are exhibited for typical values of Jo/J1.
format	Article
author	Ganikhodjaev, Nasir Temir, Seyit Akin, Hasan
author_facet	Ganikhodjaev, Nasir Temir, Seyit Akin, Hasan
author_sort	Ganikhodjaev, Nasir
title	Modulated phase of a Potts Model with competing binary interactions on a Cayley tree
title_short	Modulated phase of a Potts Model with competing binary interactions on a Cayley tree
title_full	Modulated phase of a Potts Model with competing binary interactions on a Cayley tree
title_fullStr	Modulated phase of a Potts Model with competing binary interactions on a Cayley tree
title_full_unstemmed	Modulated phase of a Potts Model with competing binary interactions on a Cayley tree
title_sort	modulated phase of a potts model with competing binary interactions on a cayley tree
publisher	Springer Link
publishDate	2009
url	http://irep.iium.edu.my/1639/ http://irep.iium.edu.my/1639/ http://irep.iium.edu.my/1639/ http://irep.iium.edu.my/1639/1/Modulated-phase-of-a-potts-model-with-competing-binary-interactions-on-a-cayley-tree_2009_Journal-of-Statistical-Physics.pdf
first_indexed	2023-09-18T20:09:03Z
last_indexed	2023-09-18T20:09:03Z
_version_	1777407354617200640

Modulated phase of a Potts Model with competing binary interactions on a Cayley tree

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