Molecular-dynamics study of melting in two dimensions. Inverse-twelfth-power interaction

Results of a molecular-dynamics computer simulation of the solid-fluid transition in two dimensions for a system of 780 particles interacting with a purely repulsive $r^{-12\mathrm{}}$ pair potential are presented. The pressure as a function of density along the $T=1\mathrm{}$ isotherm has a narrow nonmonotonic region with a symmetric loop, indicative of a weak first-order melting transition. This identification and the location of the transition is in good agreement with that obtained from an analysis of the free energies of the fluid and solid phases. Equilibration problems are found in the solid phase and the melting of a defective solid is also investigated. The behavior of the pair distribution function, angular correlation function, diffusion constant, and the defect structure uncovered by an analysis of nearest-neighbor polygons is generally consistent with a first-order mechanism. Evidence for direct fluid-solid coexistence is presented. However, a very small fluid-solid interface tension is indicated, and there is a rapid growth in the range of correlations in the fluid near freezing. The behavior of the elastic constants at melting is in fairly good agreement with the Halperin-Nelson melting criterion.