CRITICAL PROPERTIES OF THE BLUME-EMERY-GRIFFITHS MODEL FROM THE COHERENT-ANOMALY METHOD

We obtain the behaviour of the critical exponent gamma in the Blume-Em ery-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 me an-field approximations. Even the minimal hierarchy of self-consistent approximations, provided by the cluster-variation method, yields very accurate estimates of gamma and critical temperatures, except close t o the ordinary tricritical points, where the corrections to the classi cal value of gamma are very small. This also demonstrates the very goo d convergence of the cluster-variation approximations to the exact val ue.