| Efficiency of rejection-free dynamic Monte Carlo methods for homogeneous spin models, hard disk systems, and hard sphere systems (2006) | |||||||||||||
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(constβ) in the Ising, √β in the classical XY, and βin the classical Heisenberg spin systems with inverse temperature β, regardless of the dimension. The efficiency in hard particle systems is also obtained, and found to be proportional to (ρ_{cp} −ρ)^{−d} with the closest packing density ρ_{cp}, density ρ, 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.. Physical Review E 74(2), 2006, 026707 | |||||||||||||
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