Short-range order in Ising-like models with many-body interactions: Description via effective pair interactions

The validity of approximating the effects of many-body interactions in Ising-type models by several types of pair interactions is examined. In addition to the bare pair interaction (P0), two interactions derived via high-temperature approximations are considered. The first (P1) is concentration dependent and is obtained by an expansion to first order in inverse temperature; the second (P2), obtained by a second-order expansion, is both temperature and concentration dependent. The validity of the pair approximations is evaluated by Monte Carlo calculations of ordering and thermodynamic properties for a particular many-body interaction model on a fcc lattice. In the high-temperature limit, the structure (as described by pair and multiple correlation functions) is accurately obtained by both the interactions P1 and P2, but not by P0. Over a much wider range of temperatures, P2 still yields accurate results. However, none of the pair interaction models obtain accurate mixing enthalpies. The connections that are derived between the strength of the many-body interactions, and the environmental dependence of the effective pair interactions, provide a possible way of evaluating the importance of the many-body interactions in solid solutions from diffuse scattering measurements.