  A molecular dynamics study of a two dimensional system of particles
interacting through a Lennard-Jones pairwise potential is performed at fixed
temperature and vanishing external pressure. As the temperature is increased, a
solid-to-liquid transition occurs. When the melting temperature $T_c$ is
approached from below, there is a proliferation of dislocation pairs and the
elastic constant approaches the value predicted by the KTHNY theory. In
addition, as $T_c$ is approached from above, the relaxation time increases,
consistent with an approach to criticality. However, simulations fail to
produce a stable hexatic phase using systems with up to 90,000 particles. A
significant jump in enthalpy at $T_c$ is observed, consistent with either a
first order or a continuous transition. The role of external pressure is
discussed.
