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

Abstract

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.