| In this work we present a numerical study, based on molecular dynamics simulations, to estimate the freezing point of hard spheres and hypersphere systems in dimension D=4, 5, 6 and 7. To do so we have studied the changes of the Radial Distribution Function (RDF) as a function of density in the coexistence region. We started our simulations from crystalline states, with densities above the melting point, and moved down to densities in the liquid state below the freezing point. We observed, for all the examined dimensions (including D=3) that the height of first minimum of the RDF changes in a continuous way, but resembles a second order phase transition around the freezing density. With these results we propose a numerical method to estimate the freezing point as a function of the dimension D using numerical fits and semiempirical approaches. We find that the values obtained for the freezing point are very close to simulations and theoretical approaches up to D=5 reinforcing the validity of the proposed method. The method was also applied to numerical simulations for D=6 and D=7 giving new estimations of the freezing point at those dimensionalities. |
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