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(constβ) in the Ising, β in the classical XY, and β in 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 (ρcp-ρ)-d with the closest packing density ρcp , 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.
- Publication:
-
Physical Review E
- Pub Date:
- August 2006
- DOI:
- 10.1103/PhysRevE.74.026707
- arXiv:
- arXiv:cond-mat/0312548
- Bibcode:
- 2006PhRvE..74b6707W
- Keywords:
-
- 02.70.Tt;
- 75.10.Hk;
- 02.50.Ga;
- Justifications or modifications of Monte Carlo methods;
- Classical spin models;
- Markov processes;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 8 pages, 9 figures. This paper has been combined into the cond-mat/0508652, and published in Phys. Rev. E