Effective Many-Body Interactions in Dipolar Fluids and their Effect on Structure: Can the Dipole-Dipole Interaction be Modelled as a Short-Ranged 3-Body Interaction?

In the 1970s, Stell {\it et al.} showed that it is possible to map the partition function of a system of particles interacting via anisotropic dipolar pairwise interactions to that of a hypothetical system with isotropic many-body interactions. It follows that ``polar and nonpolar fluids have the same critical exponents'' irrespective of long-ranged Coulombic interactions. We have calculated the structural properties of a system of soft spheres with the leading-order 2- and 3-body terms of the isotropic many-body potential. We have compared radial distribution functions and structure factors obtained from $NVT$ Monte Carlo simulations with those from molecular dynamics simulations of dipolar soft spheres (DSSs) under the same physical conditions. We find that the many-body potential overemphasises chaining when compared to the equivalent DSS system. The chain-inducing component is the three-body Axilrod-Teller potential, and by adjusting its contribution, it is possible to match the structure with that of the DSS fluid, showing that the many-body potential can be used as a proxy for the dipolar potential. We conclude by studying the gas-liquid phase transition, finding that the phase transition disappears beyond a threshold degree of chaining.