Cluster vs Single-Spin Algorithms -- Which are More Efficient?

Details Cluster vs Single-Spin Algorithms -- Which are More Efficient? Cluster vs Single-Spin Algorithms -- Which are More Efficient?

1993-04-07

arxiv.org/abs/cond-mat/9304008v1

Physics

Condensed Matter

13pages, postscript file, HLRZ 21/93

Scientific paper

A comparison between single-cluster and single-spin algorithms is made for the Ising model in 2 and 3 dimensions. We compare the amount of computer time needed to achieve a given level of statistical accuracy, rather than the speed in terms of site updates per second or the dynamical critical exponents. Our main result is that the cluster algorithms become more efficient when the system size, $L^d$, exceeds, $L\sim 70$--$300$ for $d=2$ and $L\sim 80$--$200$ for $d=3$. The exact value of the crossover is dependent upon the computer being used. The lower end of the crossover range is typical of workstations while the higher end is typical of vector computers. Hence, even for workstations, the system sizes needed for efficient use of the cluster algorithm is relatively large.

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