Mean Field Behavior of Cluster Dynamics

Details Mean Field Behavior of Cluster Dynamics Mean Field Behavior of Cluster Dynamics

1996-03-20

arxiv.org/abs/cond-mat/9603134v2

Physics

Condensed Matter

Revtex, 9 pages with 7 figures

Scientific paper

10.1103/PhysRevE.54.2351

The dynamic behavior of cluster algorithms is analyzed in the classical mean field limit. Rigorous analytical results below $T_c$ establish that the dynamic exponent has the value $z_{sw}=1$ for the Swendsen-Wang algorithm and $z_{uw}=0$ for the Wolff algorithm. An efficient Monte Carlo implementation is introduced, adapted for using these algorithms for fully connected graphs. Extensive simulations both above and below $T_c$ demonstrate scaling and evaluate the finite-size scaling function by means of a rather impressive collapse of the data.

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