Influence of vacancies on the melting transition of hard disks in two dimensions

We present the results of molecular dynamics simulations of two-dimensional (2D) hard disk systems in the vicinity of melting. The simulations are used to calculate the elastic constants, which can be used to estimate the location of the Kosterlitz-Thouless dislocation unbinding transition. Simulations on defect-free lattices indicate that this transition is expected to occur at essentially the same density as a first-order solid-isotropic transition and so it is not possible to rule out either a one step weak first-order transition between the solid and the isotropic fluid or a two step transition via a hexatic phase. Simulations performed on systems with vacancies indicate that the elastic constants are essentially unchanged at constant density. This result implies that vacancies have little influence on the melting of 2D hard disk solids.