Observation of a two-stage melting transition in two dimensions

We have performed hybrid Monte Carlo and molecular dynamics computer simulations to study the melting transition for a two-dimensional material consisting of classical point particles interacting via an ${\mathit{r}}^{\mathrm{\ensuremath{-}}12}$ repulsive pair potential. As the density increases, the liquid phase develops hexatic structure at values of the pressure that are too low to allow coexistence with a stable crystal possessing an equilibrium concentration of vacancies. Bond orientational order, translational order, and densities are computed for sub-blocks of the total system. Histograms of these quantities remain unimodal throughout the transition region, indicating no tendency for phase separation. Through the use of block analysis techniques, we extract exponents for the bond orientational and translational correlations in the hexatic and the solid that are consistent with the predictions of the Kosterlitz-Thouless-Halperin-Nelson-Young theory. \textcopyright{} 1996 The American Physical Society.