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

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

2005-08-29

arxiv.org/abs/cond-mat/0508652v4

Phys. Rev. E 74 026707, (2006)

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1103/PhysRevE.74.026707

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 $(\rhoc -\rho)^{-d}$ 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.

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