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

physical review e

Ground-state structures in Ising magnets on the Shastry-Sutherland  lattice with long-range interactions and fractional magnetization plateaus in  TmB4