  The phase diagram of the prototypical two-dimensional Lennard-Jones system,
while extensively investigated, is still debated. In particular, there are
controversial results in the literature as concern the existence of the hexatic
phase and the melting scenario. Here, we study the phase behaviour of 2D LJ
particles via large-scale numerical simulations. We demonstrate that at high
temperature, when the attraction in the potential plays a minor role, melting
occurs via a continuous solid-hexatic transition followed by a first-order
hexatic-fluid transition. As the temperature decreases, the density range where
the hexatic phase occurs shrinks so that at low-temperature melting occurs via
a first-order liquid-solid transition. The temperature where the hexatic phase
disappears is well above the liquid-gas critical temperature. The evolution of
the density of topological defects confirms this scenario.
