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We construct a rejection-free Monte Carlo method for the hard-disk system.Rejection-free Monte Carlo methods preserve the time-evolution behavior of thestandard Monte Carlo method, and this relationship is confirmed for our methodby observing nonequilibrium relaxation of a bond-orientational order parameter.The rejection-free method gives a greater computational efficiency than thestandard method at high densities. The rejection free method is implemented ina shrewd manner using optimization methods to calculate a rejection probabilityand to update the system. This method should allow an efficient study of thedynamics of two-dimensional solids at high density.Comment: 8 pages, 9 figures. This paper has been combined into the  cond-mat/0508652, and published in Phys. Rev.

Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems