We investigate the thermal variations of the spin-1 Blume-Emergy-Griffiths model with the repulsive biquadratic interaction by using the lowest approximation of the cluster-variation method. Besides the stable branches of the order parameters, we obtain the metastable and unstable parts of these curves and also find phase transitions of the metastable branches of the order parameters. The classification of the stable, metastable, and unstable states is made by comparing the free-energy values of these states. We also study the dynamics of the model by the path probability method in order to make sure that we find and define the metastable and unstable branches of the order parameters completely and correctly. This is done by studying the relaxation of the order parameters and as well as expressing the solution of the dynamic equations by means of the flow diagrams. Finally, we present the metastable phase diagrams in addition to the equilibrium phase diagrams in $\mathrm{}(kT/J,D/J)\mathrm{}$ and $\mathrm{}(kT/J,K/J)\mathrm{}$ planes.

• Received 10 October 2001

DOI:https://doi.org/10.1103/PhysRevB.66.054105