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29 March 2024
 
  » arxiv » cond-mat/0508652

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Efficiency of rejection free Monte Carlo methods
H. Watanabe ; S. Yukawa ; M.A. Novotny ; N. Ito ;
Date 29 Aug 2005
Subject Statistical Mechanics | cond-mat.stat-mech
AbstractWe construct asymptotic arguments for the efficiency of rejection-free Monte Carlo (RFMC) methods, and find that efficiencies are proportional to ${e}^eta$ in the Ising, $sqrt{eta}$ in the classical XY, and $eta$ in the classical Heisenberg spin systems with inverse temperature $eta$, regardless of dimensionality. The efficiencies in hard particle systems are also obtained, and found to be proportional to $( hoc - ho)^{-d}$ with the closest packing density $ hoc$, density $ ho$, and dimensionality of systems $d$. We describe in detail a RFMC method for the hard-disk system. The RFMC keeps the original dynamics constant, while simultaneously becoming much more efficient in certain regimes, such as at low temperatures for spin systems or at high densities for particle systems.
Source arXiv, cond-mat/0508652
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