Virtual Bond Percolation for Ising Cluster Dynamics

Details Virtual Bond Percolation for Ising Cluster Dynamics Virtual Bond Percolation for Ising Cluster Dynamics

1992-06-04

arxiv.org/abs/hep-lat/9206007v1

Physics

High Energy Physics

High Energy Physics - Lattice

16 pages (LaTeX), 10 PostScript figures (large file 787k)

Scientific paper

10.1016/0378-4371(93)90478-M

The Fortuin-Kasteleyn mapping between the Ising model and the site-bond correlated percolation model is shown to be only one of an infinite class of exact mappings. These new cluster representations are a result of "renormalized" percolation rules correlated to entire blocks of spins. For example these rules allow for percolation on "virtual" bonds between spins not present in the underlying Hamiltonian. As a consequence we can define new random cluster theories each with its own Monte Carlo cluster dynamics that exactly reproduce the Ising model. By tuning parameters on the critical percolation surface, it is demonstrated numerically that cluster algorithms can be formulated for the 2-d and 3-d Ising model that have smaller autocorrelations than the original Swendsen-Wang algorithm.

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