Monte Carlo Simulation of Hard Hyperspheres in Six,Seven and Eight Dimensions for Low to Moderate Densities

The pair correlation function of hard hyperspheres in six, seven and eight dimensions is obtained from Monte Carlo simulations. The value of the pair correlation function at contact is compared with the results from molecular dynamics calculations and a variety of theoretical approaches. Remarkably good agreement is found with the simple, closed-form equations of Y. Song, E. A. Mason and R. M. Stratt, J. Phys. Chem., 93:6916–6919 (1989). The Monte Carlo results for the equation of state are compared with the theoretical expressions of M. Baus and J. L. Colot, Phys. Rev. A, 36:3912 (1987), M. Luban and J. P. J. Michels, Phys. Rev A, 41:6796 (1990), and high order virial expansions. In addition, in seven dimensions, comparisons are made with the exact PY solution provided by M. Robles, M. L. de Haro and A. Santos, J. Chem. Phys., 120:9113 (2004). Very good agreement was observed between theory and computer simulation in all dimensions.