Melting in a finite, two-dimensional Yukawa system

A complex (dusty) plasma disk is a two-dimensional system of monodisperse microspheres confined by a parabolic well and interacting through a Yukawa potential. (Complex plasma is an open, dissipative sytem.) Consequently, a complex plasma disk is a physical realization of a finite, two-dimensional Yukawa system. Recent experiments on a complex plasma disk with $n \approx 3900$ dust particles [T. E. Sheridan, {\it Phys. Plasmas} {\bf 15}, 103702 (2008)] indicate that the system melts via two second-order topological phase transitions. In the present work, we will model these experimental results using the Metropolis algorithm to generate ensembles of configurations consistent with a given thermodynamic temperature. Model results will be compared with experiment. In particular, we wish to determine the exponent characterizing the power law decay of the bond-orientational correlation function in the hexatic phase, which the experimental results indicate may be greater than that predicted by KTHNY theory.