A rejection-free Monte Carlo method for the hard-disk system

We construct a rejection-free Monte Carlo method for the hard-disk system. Rejection-free Monte Carlo methods preserve the time-evolution behavior of the standard Monte Carlo method, and it is confirmed for our method by observing nonequilibrium relaxations of a bond-orientational order parameter. The rejection-free method obtains much better performance than the standard method at high densities with new optimization methods to calculate a rejection probability and to update the system. This method should allow an efficient study of the dynamics of two-dimensional solids at high density.