Local density approach for modeling fluids with density-dependent interactions

In a recent paper [Phys. Rev. Lett. 86, 2038 (2001)] a simple fluid with a particular density-dependent pair potential was shown to exhibit, together with the vapor-liquid transition, a liquid-liquid phase separation and it was evidenced that, in order to adequately define the correct boundaries of stability, a simulation procedure based on the use of local densities had to be devised. It was found that for certain thermodynamic states the potential drives the system toward a phase separation that is otherwise frustrated by the change in the interactions induced by density fluctuations. Therefore, when integral equations or global density simulations are used, the critical points estimated from the thermodynamics are not associated with divergent correlations and vice versa. Here, we will explore in depth this fluid and introduce a detailed account of the proposed local density simulation technique. The results presented bear general significance for density-dependent potentials, like those of liquid metals or charge-stabilized colloids.