Critical properties of the Blume-Emery-Griffiths model from the coherent-anomaly method

We obtain the behaviour of the critical exponent γ in the Blume-Emery-Griffiths model on the square and the triangular lattices crossing over from the spin- 1 2 Ising critical regime to the Potts and to the ordinary tricritical regime. We use the coherent-anomaly method which scales the amplitudes o...

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Bibliographic Details
Published in:Physica A 1996-11, Vol.233 (1), p.515-522
Main Authors: Grigelionis, Gintautas, Lapinskas, Saulius, Rosengren, Anders
Format: Article
Language:English
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Summary:We obtain the behaviour of the critical exponent γ in the Blume-Emery-Griffiths model on the square and the triangular lattices crossing over from the spin- 1 2 Ising critical regime to the Potts and to the ordinary tricritical regime. We use the coherent-anomaly method which scales the amplitudes of the leading divergencies obtained from the mean-field approximations. Even the minimal hierarchy of self-consistent approximations, provided by the cluster-variation method, yields very accurate estimates of γ and critical temperatures, except close to the ordinary tricritical points, where the corrections to the classical value of γ are very small. This also demonstrates the very good convergence of the cluster-variation approximations to the exact value.
ISSN:0378-4371
1873-2119
DOI:10.1016/S0378-4371(96)00238-5