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.
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