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

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics/Computer Science, Manhattan College, Manhattan College Parkway, Riverdale, New York, 10471, USA

    Marvin Bishop

  2. Department of Computer and Information Sciences, Brooklyn College, 2900 Bedford Avenue, Brooklyn, New York, 11210, USA

    Paula A. Whitlock

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  1. Marvin Bishop
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  2. Paula A. Whitlock
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Correspondence to Marvin Bishop.

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Bishop, M., Whitlock, P.A. Monte Carlo Simulation of Hard Hyperspheres in Six, Seven and Eight Dimensions for Low to Moderate Densities. J Stat Phys 126, 299–314 (2007). https://doi.org/10.1007/s10955-006-9266-9

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  • DOI: https://doi.org/10.1007/s10955-006-9266-9

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