The fluid to solid phase transition of hard hyperspheres in four and five dimensions.

Molecular dynamics and Monte Carlo simulations are performed for four- and five-dimensional hard hyperspheres at a variety of densities, ranging from the fluid state to the solid regime of A(4), D(4), D(4)*, and D(5) lattices. The equation of state, the radial distribution functions, and the average number of hyperspheres in a coordination layer are determined. The equations of state are in excellent agreement with values obtained from both theoretical approaches and other simulations. The results for the average number of hyperspheres in a coordination layer are in agreement with the theoretical predictions for the different lattices. The radial distribution function gives better insight about the fluid to solid transition than the equation of state.