Ground-state structures in Ising magnets on the Shastry-Sutherland lattice with long-range interactions and fractional magnetization plateaus in TmB_{4}

A method for the study of the ground states of lattice-gas models or equivalent spin models with extended-range interactions is proposed. 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 TmB_{4} regarded as a strong Ising magnet on the Shastry-Sutherland lattice with long-range interactions.