  A method for the study of the ground states of lattice-gas models or
equivalent spin models with extended-range interactions is developed. It is
shown that effect of longer-range interactions can be studied in terms of the
solution of the ground-state problem for a model with short-range interactions.
The method is applied to explain the emergence of fractional magnetization
plateaus in TmB4 that is regarded as a strong Ising magnet on the
Shastry-Sutherland lattice.
