Simulations of Two-Dimensional Melting on the Surface of a Sphere

We have simulated a system of classical particles confined on the surface of a sphere interacting with a repulsive $r^{-12}$ potential. The same system simulated on a plane with periodic boundary conditions has van der Waals loops in pressure-density plots which are usually interpreted as evidence for a first order melting transition, but on the sphere such loops are absent. We also investigated the structure factor and from the width of the first peak as a function of density we can show that the growth of the correlation length is consistent with KTHNY theory. This suggests that simulations of two dimensional melting phenomena are best performed on the surface of a sphere.