On the stability of the infinite dimensional fluid of hard hyperspheres: A statistical mechanical estimate of the density of closest packing of simple hypercubic lattices in spaces of large dimensionality

We report an analysis of the bifurcation of the solution to the nonlinear equation for the inhomogeneous singlet density in a system of hard hyperspheres; the instability examined corresponds to the liquid-to-simple hypercubic lattice transition. We propose that in the limit d→∞ the continuous bifurcation which occurs is at the maximum achievable density in a simple hypercubic lattice. Extension of this result to 1