Monte Carlo calculations for 108hyphen; and 256hyphen;particle Lennardhyphen;Jones systems have been carried out at 140 temperaturehyphen;density points in the vicinity of the fluidhyphen;solid phase transition. Several types of initial configurations have been used, including fcc lattice arrays, disordered arrays, and combinations of lattice and disordered arrays. The results of runs at high densities show that for small periodic systems the calculations are dependent on the initial configuration and that such systems can exist in many different metastable states from which minimum energy states are not accessible in runs of the order of 106to 107configurations. In the vicinity of the smallest density at which the fcc lattice is stable, the calculated pressurehyphen;volume curve exhibits many of the features of a ``van der Waals loop''; however, because a single phase is thermodynamically unstable over part of this region, the loop cannot be completely resolved through machine calculations. The use of the van der Waals loop to estimate the melting parameters for the Lennardhyphen;Jones system leads to fluid and solid densities 3percnt; to 4percnt; lower than those calculated by the indirect method of Hansen and Verlet.
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