Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions

Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions

We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jpand one-level next-nearest neighbour interactions J. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1and prolonged next-nearest nei...

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Main Authors: Ganikhodjaev, Nasir, Zakaria, Siti Fatimah
Format: Conference or Workshop Item
Language:English
Published: 2011
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/7278/
http://irep.iium.edu.my/7278/
http://irep.iium.edu.my/7278/2/LIMIT_BEHAVIOR_OF_DYNAMIC_SYSTEMS_CORRESPONDING_TO_LATTICE_MODELS_WITH_COMPETING_PROLONGED_AND_ONE-LEVEL_BINARY_INTERACTIONS.pdf
id iium-7278
recordtype eprints
spelling iium-72782019-11-20T08:04:08Z http://irep.iium.edu.my/7278/ Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary 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 Jpand one-level next-nearest neighbour interactions J. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1and prolonged next-nearest neighbour interactions Jpcontains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with J ≠ 0. For given lattice model on a Cayley tree, i.e., Jp≠ 0; J ≠ 0 with J1= 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1and show that the class of modulated phases consists of so-called antiphase with period 4 only. 2011-01 Conference or Workshop Item NonPeerReviewed application/pdf en http://irep.iium.edu.my/7278/2/LIMIT_BEHAVIOR_OF_DYNAMIC_SYSTEMS_CORRESPONDING_TO_LATTICE_MODELS_WITH_COMPETING_PROLONGED_AND_ONE-LEVEL_BINARY_INTERACTIONS.pdf Ganikhodjaev, Nasir and Zakaria, Siti Fatimah (2011) Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions. In: IIUM Research, Invention and Innovation Exhibition (IRIIE) 2011, 9-10 February 2011, Cultural Activity Centre (CAC) and KAED Gallery IIUM. (Unpublished) http://www.iium.edu.my/irie/11/
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
Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions
description We study the phase diagram of the Ising model on a Cayley tree with competing prolonged next-nearest neighbour Jpand one-level next-nearest neighbour interactions J. Vannimenus proved that the phase diagram of Ising model with competing neareast-neighbour interaction J1and prolonged next-nearest neighbour interactions Jpcontains a modulated phase, as found for similar models on periodic lattices. Later Mariz et al generalized this result for Ising model with J ≠ 0. For given lattice model on a Cayley tree, i.e., Jp≠ 0; J ≠ 0 with J1= 0 we describe phase diagram and clarify the role of nearest-neighbour interaction J1and show that the class of modulated phases consists of so-called antiphase with period 4 only.
format Conference or Workshop Item
author Ganikhodjaev, Nasir
Zakaria, Siti Fatimah
author_facet Ganikhodjaev, Nasir
Zakaria, Siti Fatimah
author_sort Ganikhodjaev, Nasir
title Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions
title_short Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions
title_full Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions
title_fullStr Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions
title_full_unstemmed Limit behavior of dynamic systems corresponding to Lattice models with competing prolonged and one-level binary interactions
title_sort limit behavior of dynamic systems corresponding to lattice models with competing prolonged and one-level binary interactions
publishDate 2011
url http://irep.iium.edu.my/7278/
http://irep.iium.edu.my/7278/
http://irep.iium.edu.my/7278/2/LIMIT_BEHAVIOR_OF_DYNAMIC_SYSTEMS_CORRESPONDING_TO_LATTICE_MODELS_WITH_COMPETING_PROLONGED_AND_ONE-LEVEL_BINARY_INTERACTIONS.pdf
first_indexed 2023-09-18T20:16:35Z
last_indexed 2023-09-18T20:16:35Z
_version_ 1777407828653244416

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