Asymptotic Behavior for the Particle Distribution Function of Simple Fluids near the Critical Point

Classical single-component fluids are considered in order to investigate the asymptotic behavior of the joint distribution function of l+m particles, ρl+m, for large separation between the set of l and m particles. Near the critical point the authors find ρl+m to be the product of ρl and ρm plus the long-range corrections. The critical singularities, such as the heat capacity at constant volume, are explained in terms of the authors' result on the asymptotic distribution function.