Kinematics of multigrid Monte Carlo |
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Authors: | Martin Grabenstein Klaus Pinn |
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Institution: | (1) II. Institut für Theoretische Physik, Universität Hamburg, W-2000 Hamburg 50, Germany;(2) Institut für Theoretische Physik I, Universität Münster, W-4400 Münster, Germany |
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Abstract: | We study the kinematics of multigrid Monte Carlo algorithms by means of acceptance rates for nonlocal Metropolis update proposals. An approximation formula for acceptance rates is derived. We present a comparison of different coarse-to-fine interpolation schemes in free field theory, where the formula is exact. The predictions of the approximation formula for several interacting models are well confirmed by Monte Carlo simulations. The following rule is found: For a critical model with fundamental Hamiltonianþ( ), the absence of critical slowing down can only be expected if the expansion of þ( + ) in terms of the shift contains no relevant (mass) term. We also introduce a multigrid update procedure for non-abelian lattice gauge theory and study the acceptance rates for gauge groupSU(2) in four dimensions. |
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Keywords: | Computer simulations critical slowing down multigrid Monte Carlo algorithms acceptance rates spin models lattice gauge theory |
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