Melting in two dimensions: Determination of phase transition boundaries

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Abstract
Molecular dynamics computations are reported for systems of soft repulsive discs of the inverse twelfth‐power potential and for Lennard‐Jones atoms in two dimensions. In the case of soft discs the melting transition is obtained by assuming a first‐order transition and subsequent application of Ross’s melting rule. The assumption is vindicated by additional computations for the 2‐D L‐J model in which the melting and freezing parameters are determined by direct MD computation along the isotherm T=0.8 ε/k and the isochore ρr20=1.0079. The results reaffirm the presence of first‐order phase boundaries and refute the postulated existence of a ’’hexatic mesophase’’ bounded by second‐order transitions. These two‐dimensional models are seen to have much smaller discontinuities in density and entropy than their three‐dimensional counterparts and to exhibit more pronounced premelting increases in the heat capacity. This is interpreted to be a consequence of the proximity of the mechanical instability points to the first‐order thermodynamic melting transition for these two‐dimensional systems. Previously reported lambdalike behavior of the heat capacity through the melting transition of the 2‐D one‐component plasma is consistent with this interpretation for an irreversible isochoric traversal of a two‐phase region and hence suggests an ordinary, albeit weaker, first‐order melting transition in this system also.