One-Stage Continuous Melting Transition in Two Dimensions

Monte Carlo results are reported for melting of two-dimensional systems of N hard disks for various values of N. Runs of up to 10⁸ Monte Carlo sweeps give the following equilibrium results: (1) there is a single second-order transition at volume υc0ex0ex=0ex0ex1.260±0.005; (2) the orientational order parameter drops discontinuously to zero at υ0ex0ex=0ex0exυc; (3) η₆0ex0ex=0ex0ex0.30±0.05 at υ0ex0ex=0ex0exυc; (4) there is consistency with ξ0ex0ex=0ex0exexp(b/u1/2) in the isotropic phase, where u0ex0ex=0ex0exυ-υc and b0.8. An intermediate phase in which the volume can vary by more than about 1% is ruled out.