First-order melting transition of the hard-disk system

We present a very strong evidence for a first-order melting transition in the hard-disk system by exploiting the finite-size scaling of the bulk free-energy barrier. We use isobaric Monte Carlo simulations to allow fluctuations in the volume of the system, which lead, in the presence of a first-order transition, to a double-peaked structure in the volume distribution. We also find that the system melts directly from a two-dimensional solid with long-range orientational order to an isotropic liquid with no intervening hexatic phase.