Nonequilibrium relaxation analysis of two-dimensional melting.

The phase diagram of a hard-disk system is studied by observing nonequilibrium relaxation functions of a bond-orientational order parameter using particle dynamics simulations. From a finite-time scaling analysis, two Kosterlitz-Thouless transitions can be observed when the density is increased from the isotropic fluid phase to closest packing. The transition densities are estimated to be 0.901(2) and 0.910(2), where the density denotes the fraction of area occupied by the particles, the density is normalized to one for the quadratic packing configuration. These observations are consistent with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory.