Efficiency of Rejection-Free Monte Carlo Algorithms for Particles Systems

We calculated the efficiency of rejection-free methods for dynamic Monte Carlo studies of off-lattice systems. Following the methodology of Watanabe et al\footnote{\label{watanabe}H. Watanabe, S. Yukawa, M.A. Novotny and N. Ito, \textit{Efficiency of Rejection-free dynamic Monte Carlo methods for homogenous spin models, hard disk systems, and hard sphere system}, Phys. Rew. E, \textbf{74}, 026707 (2006)}, we studied $d=1$ particles models including the hard rod model, and models with both harmonic and Lennard-Jones potentials. The hard-rod results are in agreement with [1], namely the efficiency near the close-packing density $\rho_{_{cp}}$ is proportional to $(\rho_{_{cp}}-\rho)^{-d}$, where $d$ is the dimension of the system and $\rho$ the system density. We also report on the algorithmic efficiency for cases with heterogenous particles. Some results in $d=2$ will also be presented.