Large-scale simulations of the two-dimensional melting of hard disks

Large-scale computer simulations with more than four million particles have been performed to study the melting transition in a two-dimensional hard disk fluid. The van der Waals loop previously observed in the pressure-density relationship of smaller simulations is shown to disappear systematically with increase in sample size, but even with these large system sizes, the freezing transition still exhibits what appears to be weakly first-order behavior, though the scaling of the bond orientation order is consistent with the Halperin-Nelson-Young picture. Above this freezing transition region, scaling analysis of the translational order yields a lower bound for the melting density that is much higher than previously thought and provides compelling evidence that the solid phase first melts into a hexatic phase via a continuous transition, before it goes into the isotropic phase.