Ising model with restricted interactions on general Cayley tree of arbitrary order

We study an Ising model on a general Cayley tree with competing interaction of next-nearest-neighbour of two types; prolonged and one-level k-tuple interactions. Vannimenus covers a study of Ising model on competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interaction J...

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Main Authors:	Ganikhodjaev, Nasir, Zakaria, Siti Fatimah
Format:	Article
Language:	English
Published:	INSI Publications 2011
Subjects:	QA Mathematics QC Physics
Online Access:	http://irep.iium.edu.my/7134/ http://irep.iium.edu.my/7134/ http://irep.iium.edu.my/7134/1/with_Fatima_1296-1304.pdf

id	iium-7134
recordtype	eprints
spelling	iium-71342019-11-20T08:07:52Z http://irep.iium.edu.my/7134/ Ising model with restricted interactions on general Cayley tree of arbitrary order Ganikhodjaev, Nasir Zakaria, Siti Fatimah QA Mathematics QC Physics We study an Ising model on a general Cayley tree with competing interaction of next-nearest-neighbour of two types; prolonged and one-level k-tuple interactions. Vannimenus covers a study of Ising model on competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interaction Jp. Later Mariz et al extend Vannimenus work by adding a one-level interaction Jo for order 2 with the existence of external magnetic field. And recently Ganikhodjaev et al found only simple modulated phases exist for Ising model with second neighbour prolonged and one-level competing interaction of order 2. So, in this paper, we study the Ising model with competing interaction J0≠0, Jp≠0 and J1=0 to identify the preservation of those phases for higher order k. We derived two types of general system of equations and describe the phase diagram for both cases of even and odd order. INSI Publications 2011 Article PeerReviewed application/pdf en http://irep.iium.edu.my/7134/1/with_Fatima_1296-1304.pdf Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2011) Ising model with restricted interactions on general Cayley tree of arbitrary order. Australian Journal of Basic and Applied Sciences, 5 (8). pp. 1296-1304. ISSN 1991-8178 http://www.insipub.com/ajbas/2011/August-2011/1296-1304.pdf
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English
topic	QA Mathematics QC Physics
spellingShingle	QA Mathematics QC Physics Ganikhodjaev, Nasir Zakaria, Siti Fatimah Ising model with restricted interactions on general Cayley tree of arbitrary order
description	We study an Ising model on a general Cayley tree with competing interaction of next-nearest-neighbour of two types; prolonged and one-level k-tuple interactions. Vannimenus covers a study of Ising model on competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interaction Jp. Later Mariz et al extend Vannimenus work by adding a one-level interaction Jo for order 2 with the existence of external magnetic field. And recently Ganikhodjaev et al found only simple modulated phases exist for Ising model with second neighbour prolonged and one-level competing interaction of order 2. So, in this paper, we study the Ising model with competing interaction J0≠0, Jp≠0 and J1=0 to identify the preservation of those phases for higher order k. We derived two types of general system of equations and describe the phase diagram for both cases of even and odd order.
format	Article
author	Ganikhodjaev, Nasir Zakaria, Siti Fatimah
author_facet	Ganikhodjaev, Nasir Zakaria, Siti Fatimah
author_sort	Ganikhodjaev, Nasir
title	Ising model with restricted interactions on general Cayley tree of arbitrary order
title_short	Ising model with restricted interactions on general Cayley tree of arbitrary order
title_full	Ising model with restricted interactions on general Cayley tree of arbitrary order
title_fullStr	Ising model with restricted interactions on general Cayley tree of arbitrary order
title_full_unstemmed	Ising model with restricted interactions on general Cayley tree of arbitrary order
title_sort	ising model with restricted interactions on general cayley tree of arbitrary order
publisher	INSI Publications
publishDate	2011
url	http://irep.iium.edu.my/7134/ http://irep.iium.edu.my/7134/ http://irep.iium.edu.my/7134/1/with_Fatima_1296-1304.pdf
first_indexed	2023-09-18T20:16:25Z
last_indexed	2023-09-18T20:16:25Z
_version_	1777407817846620160

Ising model with restricted interactions on general Cayley tree of arbitrary order

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