Complete catalog of ground-state diagrams for the general three-state lattice-gas model with nearest-neighbor interactions on a square lattice

The ground states of the general three-state lattice-gas (equivalently, $S=1$ Ising) model with nearest-neighbor interactions on a square lattice are explored in the full, five-dimensional parameter space of three interaction constants and two generalized chemical potentials or fields. The resulting, complete catalog of fifteen topologically different ground-state diagrams (zero-temperature phase diagrams) is discussed in both lattice-gas and Ising-spin language. The results extend those of a recent study in a reduced parameter space [V. F. Fefelov, et al., Phys. Chem. Chem. Phys., 2018, 20, 10359--10368], which identified six different ground-state diagrams.