Density functional theory of freezing for hexagonal symmetry: Comparison with Landau theory

Density functional theory, studied recently by us [J. Chem. Phys. 87, 5449 (1987)] is used to study the freezing of hard disks and hard spheres into crystals with hexagonal symmetry. Two different numerical techniques are used, namely a Gaussian approximation to the crystal density and a more general Fourier expansion of the crystal density. The results from these methods are compared with each other, more approximate versions of density functional theory, and computer simulations. In addition, we compare density functional theory with Landau theories of first order transitions, in which the free energy is expanded as a power series, usually in just one order parameter. We find that traditional Landau theory has little validity when applied to the freezing transition.