Phase diagram of the Ising model with next-nearest-neighbour interactions

We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jp and one-level next-nearest neighbour interactions J0. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1 and prolonged next-nearest...

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Main Authors:	Ganikhodjaev, Nasir, Zakaria, Siti Fatimah
Format:	Book Chapter
Language:	English
Published:	Faculty of Engineering, International Islamic University Malaysia (IIUM) 2010
Subjects:	QA Mathematics
Online Access:	http://irep.iium.edu.my/14382/ http://irep.iium.edu.my/14382/1/ICMAE%2710_NG_SF.pdf

id	iium-14382
recordtype	eprints
spelling	iium-143822019-11-20T08:05:09Z http://irep.iium.edu.my/14382/ Phase diagram of the Ising model with next-nearest-neighbour interactions Ganikhodjaev, Nasir Zakaria, Siti Fatimah QA Mathematics We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jp and one-level next-nearest neighbour interactions J0. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1 and prolonged next-nearest neighbour interactions Jp contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo … 0. For given lattice model on a Cayley tree, i.e., Jp … 0; Jo … 0 with J1 = 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1 and show that the class of modulated phases consists of socalled antiphase with period 4 only Faculty of Engineering, International Islamic University Malaysia (IIUM) 2010-08-03 Book Chapter PeerReviewed application/pdf en http://irep.iium.edu.my/14382/1/ICMAE%2710_NG_SF.pdf Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2010) Phase diagram of the Ising model with next-nearest-neighbour interactions. In: Proceedings of International Conference on Mathematical Applications in Engineering. Faculty of Engineering, International Islamic University Malaysia (IIUM), Kuala Lumpur, pp. 355-359. ISBN 9789834309046
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 Zakaria, Siti Fatimah Phase diagram of the Ising model with next-nearest-neighbour interactions
description	We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jp and one-level next-nearest neighbour interactions J0. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1 and prolonged next-nearest neighbour interactions Jp contains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo … 0. For given lattice model on a Cayley tree, i.e., Jp … 0; Jo … 0 with J1 = 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1 and show that the class of modulated phases consists of socalled antiphase with period 4 only
format	Book Chapter
author	Ganikhodjaev, Nasir Zakaria, Siti Fatimah
author_facet	Ganikhodjaev, Nasir Zakaria, Siti Fatimah
author_sort	Ganikhodjaev, Nasir
title	Phase diagram of the Ising model with next-nearest-neighbour interactions
title_short	Phase diagram of the Ising model with next-nearest-neighbour interactions
title_full	Phase diagram of the Ising model with next-nearest-neighbour interactions
title_fullStr	Phase diagram of the Ising model with next-nearest-neighbour interactions
title_full_unstemmed	Phase diagram of the Ising model with next-nearest-neighbour interactions
title_sort	phase diagram of the ising model with next-nearest-neighbour interactions
publisher	Faculty of Engineering, International Islamic University Malaysia (IIUM)
publishDate	2010
url	http://irep.iium.edu.my/14382/ http://irep.iium.edu.my/14382/1/ICMAE%2710_NG_SF.pdf
first_indexed	2023-09-18T20:23:34Z
last_indexed	2023-09-18T20:23:34Z
_version_	1777408267169824768

Phase diagram of the Ising model with next-nearest-neighbour interactions

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