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-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 gamma and critical temperatures, except close to the ordinary tricritical points, where the corrections to the classical value of gamma are very small. This also demonstrates the very good convergence of the cluster-variation approximations to the exact value.