Nonuniform classical fluid at high dimensionality

We investigate the existence of nonuniform thermodynamic states of classical fluids with purely repulsive finite-range interaction, such as that of hard spheres. Both free energy and nonuniform profile are obtained in the strict limit of an infinitely large spatial dimension. We establish the density at which the uniform state undergoes a Kirkwood instability, and provide a basis for the surmise that this instability leads continuously to an ordered lattice.