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

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

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	4430/30004
Uncontrolled Keywords:	Blume-Emery-Griffiths model · phase transition · crystal-field interaction · Gibbs measure · recurrence equations
Subjects:	Q Science > QA Mathematics
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User:	Prof. Nasir Ganikhodjaev
Date Deposited:	02 Aug 2013 16:09
Last Modified:	02 Aug 2013 16:09
URI:	http://irep.iium.edu.my/id/eprint/30004

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