Convergence Rates of a Dynamic Monte Carlo Rejection-Free Method for Interacting particles

ORAL

Abstract

We calculated the efficiency of a Rejection-Free Monte Carlo method\footnote{H. Watanawe, S. Yukawa, M.A. Novotny and N. Ito, \textit{Efficiency of Rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere system}, Phys. Rew. E, \textbf{74}, 026707 (2006)} in the limit of low temperatures and/or high densities for $d$-dimensional particles interacting through a repulsive power-law $r^p$ as well as Lennard-Jones Interactions. Theoretically we find the algorithmic efficiency is proportional to $\rho^{\frac{p+2}{2}}T^{-\frac{d}{2}}$ where $\rho$ is the particle density and T the temperature. For different powers ($p$) in 1, 2 and 3 dimensions as a function of $T$ and $\rho$, we report results in agreement with our theoretical predictions

–

Authors

  • Marta Guerra

    • Physics and HPC2 Center for Computational Sciences, Mississippi State University

  • M.A. Novotny

    • Physics and HPC2 Center for Computational Sciences, Mississippi State University
    • Mississippi State University
    • Mississippi State U.

  • Hiroshi Watanabe

    • Department of Applied Physics, University of Tokyo
    • Nagoya University

  • Nobuyasu Ito

    • Department of Applied Physics, University of Tokyo