20-02U

A simple cluster method is used for constructing ground-state diagrams of the most general spin-1 Ising model on the unfrustrated lattices and also on the triangular and kagome lattices with nearest-neighbor interaction. On the base of notion of incompatibility for cluster configurations the boundaries between phases which correspond to first order phase transitions are found. The same model is considered on the square lattice with nearest- and next-to-nearest-neighbor interactions (without constructing ground-state phase diagrams).