The blume-emery-griffiths model on Cayley tree and its phase transitions

The blume-emery-griffiths model on Cayley tree and its phase transitions

We consider simple version of the Blume-Emery-Griffiths model on the Cayley tree and investigate the problem of phase transition using the exact recursion equations for the Cayley tree of second order, so that every spin has three nearest neighbours. These equations are studied analytical-ly for D&g...

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Main Authors: Ganikhodjaev, Nasir, Idris, Amin
Format: Article
Language:English
Published: International Digital Organization for Scientific Information 2013
Subjects:
QA Mathematics
Online Access:http://irep.iium.edu.my/30004/
http://irep.iium.edu.my/30004/
http://irep.iium.edu.my/30004/
http://irep.iium.edu.my/30004/1/Middle_East_Journal_Amin.pdf
id iium-30004
recordtype eprints
spelling iium-300042013-08-02T08:09:57Z http://irep.iium.edu.my/30004/ The blume-emery-griffiths model on Cayley tree and its phase transitions Ganikhodjaev, Nasir Idris, Amin QA Mathematics We consider simple version of the Blume-Emery-Griffiths model on the Cayley tree and investigate the problem of phase transition using the exact recursion equations for the Cayley tree of second order, so that every spin has three nearest neighbours. These equations are studied analytical-ly for D>0 and J>0. It is proved that one can reach phase transition if the reduced crystal-field interaction D/J≤2. It is found the exact value for the critical temperature Tc = (ln(2+√3))-1J/kB and described the region RA of phase transition. On the other hand it is described the phase transition region RN for considered model using numerical methods, namely, we consider three limiting Gibbs measures with different boundary conditions and if at least two of them are different then we have phase transition. It is compared the phase transition regions RA and RA. International Digital Organization for Scientific Information 2013-04 Article PeerReviewed application/pdf en http://irep.iium.edu.my/30004/1/Middle_East_Journal_Amin.pdf Ganikhodjaev, Nasir and Idris, Amin (2013) The blume-emery-griffiths model on Cayley tree and its phase transitions. Middle-East Journal of Scientific Research, 13. pp. 83-89. ISSN 1990-9233 http://www.idosi.org/mejsr/mejsr13(mae)13/13.pdf 10.5829/idosi.mejsr.2013.13.mae.99932
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
Idris, Amin
The blume-emery-griffiths model on Cayley tree and its phase transitions
description We consider simple version of the Blume-Emery-Griffiths model on the Cayley tree and investigate the problem of phase transition using the exact recursion equations for the Cayley tree of second order, so that every spin has three nearest neighbours. These equations are studied analytical-ly for D>0 and J>0. It is proved that one can reach phase transition if the reduced crystal-field interaction D/J≤2. It is found the exact value for the critical temperature Tc = (ln(2+√3))-1J/kB and described the region RA of phase transition. On the other hand it is described the phase transition region RN for considered model using numerical methods, namely, we consider three limiting Gibbs measures with different boundary conditions and if at least two of them are different then we have phase transition. It is compared the phase transition regions RA and RA.
format Article
author Ganikhodjaev, Nasir
Idris, Amin
author_facet Ganikhodjaev, Nasir
Idris, Amin
author_sort Ganikhodjaev, Nasir
title The blume-emery-griffiths model on Cayley tree and its phase transitions
title_short The blume-emery-griffiths model on Cayley tree and its phase transitions
title_full The blume-emery-griffiths model on Cayley tree and its phase transitions
title_fullStr The blume-emery-griffiths model on Cayley tree and its phase transitions
title_full_unstemmed The blume-emery-griffiths model on Cayley tree and its phase transitions
title_sort blume-emery-griffiths model on cayley tree and its phase transitions
publisher International Digital Organization for Scientific Information
publishDate 2013
url http://irep.iium.edu.my/30004/
http://irep.iium.edu.my/30004/
http://irep.iium.edu.my/30004/
http://irep.iium.edu.my/30004/1/Middle_East_Journal_Amin.pdf
first_indexed 2023-09-18T20:44:02Z
last_indexed 2023-09-18T20:44:02Z
_version_ 1777409555684130816

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