Hard-sphere and hard-disk freezing from the differential formulation of the generalized effective liquid approximation

We apply the differential formulation of the generalized effective liquid approximation to the study of hard-sphere and hard-disk freezing. We show that the thermodynamic properties of the solid phase are rather insensitive to the compressibility factor of the fluid phase used to map the solid onto the effective liquid. The solid-fluid coexistence data instead are quite dependent on the equation of state describing the fluid phase. Very accurate results, as compared with the simulation data, are obtained for both the freezing of hard spheres and hard disks.