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

Abstract

We construct asymptotic arguments for the relative efficiency of rejection-free Monte Carlo (MC) methods compared to the standard MC method. We find that the efficiency is proportional to $\exp (const\beta )$ in the Ising, $\sqrt{\beta }$ in the classical XY, and $\beta$ in the classical Heisenberg spin systems with inverse temperature $\beta$, regardless of the dimension. The efficiency in hard particle systems is also obtained, and found to be proportional to $(\rhoc -ρ)^{-d}$ with the closest packing density $\rhoc$, density $\rho$, and dimension $d$ of the systems. We construct and implement a rejection-free Monte Carlo method for the hard-disk system. The RFMC has a greater computational efficiency at high densities, and the density dependence of the efficiency is as predicted by our arguments.

12 pages, REVTEX, 13 figures, published in Phys. Rev. E

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Cited by in corpus (1)

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