  Melting in two spatial dimensions, as realized in thin films or at
interfaces, represents one of the most fascinating phase transitions in nature,
but it remains poorly understood. Even for the fundamental hard-disk model, the
melting mechanism has not been agreed on after fifty years of studies. A recent
Monte Carlo algorithm allows us to thermalize systems large enough to access
the thermodynamic regime. We show that melting in hard disks proceeds in two
steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid
transition is continuous while, surprisingly, the liquid-hexatic transition is
of first-order. This melting scenario solves one of the fundamental
statistical-physics models, which is at the root of a large body of
theoretical, computational and experimental research.
