Dual Monte Carlo and Cluster Algorithms

Details Dual Monte Carlo and Cluster Algorithms Dual Monte Carlo and Cluster Algorithms

1994-11-27

arxiv.org/abs/cond-mat/9411110v1

Physics

Condensed Matter

25 pages, 4 figures, to appear in Phys.Rev.E

Scientific paper

10.1103/PhysRevE.51.1547

We discuss the development of cluster algorithms from the viewpoint of probability theory and not from the usual viewpoint of a particular model. By using the perspective of probability theory, we detail the nature of a cluster algorithm, make explicit the assumptions embodied in all clusters of which we are aware, and define the construction of free cluster algorithms. We also illustrate these procedures by rederiving the Swendsen-Wang algorithm, presenting the details of the loop algorithm for a worldline simulation of a quantum $S=$ 1/2 model, and proposing a free cluster version of the Swendsen-Wang replica method for the random Ising model. How the principle of maximum entropy might be used to aid the construction of cluster algorithms is also discussed.

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