Cluster algorithm for hard spheres and related systems

In this paper, we present a cluster algorithm for the simulation of hard spheres and related systems. In this algorithm, a copy of the configuration is rotated with respect to a randomly chosen pivot point. The two systems are then superposed, and clusters of overlapping spheres in the joint system are isolated. Each of these clusters can be 'flipped' independently, a process which generates non-local moves in the original configuration. A generalization of this algorithm (which works perfectly well at small density) can be made to work successfully at densities around the solid-liquid transition point in the two-dimensional hard-sphere system.