Exact ground-state diagrams for the generalized Blume-Emery-Griffiths model

A simple way for constructing exact ground-state diagrams of classical spin models with nearest- or (in certain cases) also with next-to-nearest-neighbor interactions is proposed for a large class of lattices. Such diagrams are constructed for the most general spin-1 Ising model on the unfrustrated lattices with nearest-neighbor interaction. Nine topologically different diagrams are found. The same model is considered on the triangular lattice and on the square lattice with nearest- and next-to-nearest-neighbor interactions. Intermediate nonuniform phases are revealed and the conditions of their nonexistence are obtained.