Monte Carlo study of melting in two dimensions

We present the results of Monte Carlo simulations of the two-dimensional Lennard-Jones system. The energy, pressure, structure factor, elastic constants, and 〈u²〉 have been computed at several temperatures along three isochores. In addition, we have studied the distribution of disclinations and dislocations on the same isochores. There is a well-defined solid phase and a well-defined fluid phase. The nature of the transition between these two phases cannot be unambiguously determined from our data. We are also unable to determine whether or not there is a hexatic phase. Somewhat more limited data are presented for the hard-disc system. The transition between the solid and liquid phases of the system appears to be first order.