Melting in 2D lennard-jones systems: What type of phase transition?

A typical configuration of an equilibrium 2D system of 2500 Lennard-Jones particles at melting is found to be a mosaic of crystallites and amorphous clusters. This mosaic significantly changed at times around the period τ of local vibrations, while most particles retain their nearest neighbors for times much longer than τ. In a system of 2500 particles, we found no phase separation for length scales larger than that of a crystallite. With decreasing density, the number of small amorphous clusters increased, and proliferation and percolation of amorphous matter separated the crystalline-ordered parts so that correlations between local order orientations of remote crystallites disappeared. We suggest that the mosaic is a manifestation of diminished stability of the crystalline structure resulting from competition between attraction and repulsion forces.