Path-integral Monte Carlo study of the hard-disk solid.

Abstract

We present a study of the properties of the quantum two-dimensional hard-disk solid at finite temperatures using path-integral Monte Carlo simulations. We performed extensive simulations on systems with 64, 144, 256, 576, and 1024 disks. We used the image approximation for the high-temperature density matrix and ignored exchange effects. Despite the discontinuous nature of the hard-disk interaction, a long-wavelength harmonic theory provided a good model for the solid. This theory was used as a guide to study the long-range translational and orientational order of the solid at low but finite temperatures where the zero-point motion and finite-temperature excitations are both important. The properties we have computed include the particle displacements, structure factor, angular order, and density of topological defects. We compare these properties with those of the same system in the classical regime and at absolute zero, thus gaining some understanding for the crossover from classical to quantum behavior.