Dislocations and melting in two and three dimensions

Comments are presented on the recent theories of two-dimensional melting which envisage melting as proceeding via two second-order transitions comprising dislocation dipole dissociation followed by disclination dipole dissociation. It is suggested that if the configurational entropy is properly included, the model system may jump discontinuously from a volume below the dislocation transition to a volume above the disclination transition so that both transitions are virtual and are hidden in the first-order discontinuity. A reinterpretation of the recent molecular-dynamics simulation of two-dimensional melting of Frenkel and McTague, reveals that such is the case for a Lennard-Jones system. There may be no fundamental difference between two-and three-dimensional melting.