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 ($P_0$), two interactions derived via high-temperature approximations are considered. The first ($P_1$) is concentration dependent and is obtained by an expansion to first order in inverse temperature; the second ($P_2$), 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 $P_1$ and $P_2$, but not by $P_0$. Over a much wider range of temperatures, $P_2$ 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.