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:
Online Access:http://irep.iium.edu.my/14382/
http://irep.iium.edu.my/14382/1/ICMAE%2710_NG_SF.pdf
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author Ganikhodjaev, Nasir
Zakaria, Siti Fatimah
author_facet Ganikhodjaev, Nasir
Zakaria, Siti Fatimah
author_sort Ganikhodjaev, Nasir
building IIUM Repository
collection Online Access
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
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institution International Islamic University Malaysia
institution_category Local University
language English
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publishDate 2010
publisher Faculty of Engineering, International Islamic University Malaysia (IIUM)
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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
spellingShingle QA Mathematics
Ganikhodjaev, Nasir
Zakaria, Siti Fatimah
Phase diagram of the Ising model with next-nearest-neighbour interactions
title 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_short Phase diagram of the Ising model with next-nearest-neighbour interactions
title_sort phase diagram of the ising model with next-nearest-neighbour interactions
topic QA Mathematics
url http://irep.iium.edu.my/14382/
http://irep.iium.edu.my/14382/1/ICMAE%2710_NG_SF.pdf