Efficiency of Rejection-Free Methods for Dynamic Monte Carlo Studies of Off-lattice Interacting Particles

We calculate the efficiency of a rejection-free dynamic Monte Carlo method for $d$-dimensional off-lattice homogeneous particles interacting through a repulsive power-law potential $r^{-p}$. Theoretically we find the algorithmic efficiency in the limit of low temperatures and/or high densities is asymptotically proportional to ${\rho }^{\frac{p+2}{2}}{T}^{-\frac{d}{2}}$ with the particle density $\rho$ and the temperature $T$. Dynamic Monte Carlo simulations are performed in 1-, 2- and 3-dimensional systems with different powers $p$, and the results agree with the theoretical predictions.