Ferrimagnetic phases in the Blume-Emery-Griffiths model: Implications for the antiferromagnetic Potts model

The cluster-variation method is used to study the phase diagram of the Blume-Emery-Griffiths model on a simple cubic lattice. The main attention is paid to the ferrimagnetic phases occurring in a certain range of coupling parameters. A new topology, including three ferrimagnetic phases, is obtained in the vicinity of the line in parameter space where the model reduces to the antiferromagnetic three-state Potts model. The results imply the existence of three phase transitions in the antiferromagnetic Potts model.