Ising model on a general Cayley tree with competing next-nearest-neighbour interactions

Ising model on a general Cayley tree with competing next-nearest-neighbour interactions

We study the Ising model on a general Cayley tree of arbitrary order and produce the phase diagram with competing interactions prolonged next-nearest-neighbour Jp and one-level k-tuple next-nearest-neighbour Jo . Vannimenus proved the existence of modulated phase in the phase diagram of Ising model...

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Main Authors: Ganikhodjaev, Nasir, Zakaria, Siti Fatimah
Format: Conference or Workshop Item
Language:English
Published: 2011
Subjects:
QA Mathematics
QC Physics
Online Access:http://irep.iium.edu.my/1716/
http://irep.iium.edu.my/1716/
http://irep.iium.edu.my/1716/2/Ising_Model_on_a_General_Cayley_Tree_with_Competing_Next-nearest-neighbour_Interactions.pdf
id iium-1716
recordtype eprints
spelling iium-17162019-11-20T08:03:27Z http://irep.iium.edu.my/1716/ Ising model on a general Cayley tree with competing next-nearest-neighbour interactions Ganikhodjaev, Nasir Zakaria, Siti Fatimah QA Mathematics QC Physics We study the Ising model on a general Cayley tree of arbitrary order and produce the phase diagram with competing interactions prolonged next-nearest-neighbour Jp and one-level k-tuple next-nearest-neighbour Jo . Vannimenus proved the existence of modulated phase in the phase diagram of Ising model with competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interactions Jp, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo ≠ 0. For a given lattice model on a Cayley tree, i.e., Jp ≠ 0; Jo ≠ 0 with J1 = 0, we describe the general equation, phase diagram and clarify the role of nearest-neighbour interaction J1. In the presence of nearest-neighbour interaction J1, Vannimenus demonstrated that for arbitrary random initial data one can reach the same phase diagram. We show that in the case J1 = 0 the set of all possible initial data can reach different phase diagrams 2011-04 Conference or Workshop Item PeerReviewed application/pdf en http://irep.iium.edu.my/1716/2/Ising_Model_on_a_General_Cayley_Tree_with_Competing_Next-nearest-neighbour_Interactions.pdf Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2011) Ising model on a general Cayley tree with competing next-nearest-neighbour interactions. In: Annual International Conference on Operations Research and Statistics, 7-8 April 2011, Penang, Malaysia. http://dl.globalstf.org/index.php?page=shop.product_details&flypage=flypage_images.tpl&product_id=624&category_id=47&option=com_virtuemart&Itemid=4
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 on a general Cayley tree with competing next-nearest-neighbour interactions
description We study the Ising model on a general Cayley tree of arbitrary order and produce the phase diagram with competing interactions prolonged next-nearest-neighbour Jp and one-level k-tuple next-nearest-neighbour Jo . Vannimenus proved the existence of modulated phase in the phase diagram of Ising model with competing nearest-neighbour interaction J1 and prolonged next-nearest-neighbour interactions Jp, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with Jo ≠ 0. For a given lattice model on a Cayley tree, i.e., Jp ≠ 0; Jo ≠ 0 with J1 = 0, we describe the general equation, phase diagram and clarify the role of nearest-neighbour interaction J1. In the presence of nearest-neighbour interaction J1, Vannimenus demonstrated that for arbitrary random initial data one can reach the same phase diagram. We show that in the case J1 = 0 the set of all possible initial data can reach different phase diagrams
format Conference or Workshop Item
author Ganikhodjaev, Nasir
Zakaria, Siti Fatimah
author_facet Ganikhodjaev, Nasir
Zakaria, Siti Fatimah
author_sort Ganikhodjaev, Nasir
title Ising model on a general Cayley tree with competing next-nearest-neighbour interactions
title_short Ising model on a general Cayley tree with competing next-nearest-neighbour interactions
title_full Ising model on a general Cayley tree with competing next-nearest-neighbour interactions
title_fullStr Ising model on a general Cayley tree with competing next-nearest-neighbour interactions
title_full_unstemmed Ising model on a general Cayley tree with competing next-nearest-neighbour interactions
title_sort ising model on a general cayley tree with competing next-nearest-neighbour interactions
publishDate 2011
url http://irep.iium.edu.my/1716/
http://irep.iium.edu.my/1716/
http://irep.iium.edu.my/1716/2/Ising_Model_on_a_General_Cayley_Tree_with_Competing_Next-nearest-neighbour_Interactions.pdf
first_indexed 2023-09-18T20:09:10Z
last_indexed 2023-09-18T20:09:10Z
_version_ 1777407361527316480

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