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 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.