Kinematics of Multigrid Monte Carlo

Details Kinematics of Multigrid Monte Carlo Kinematics of Multigrid Monte Carlo

1992-07-03

arxiv.org/abs/hep-lat/9207003v1

J.Statist.Phys. 71 (1993) 607

Physics

High Energy Physics

High Energy Physics - Lattice

28 pages, 8 ps-figures, DESY 92-094

Scientific paper

10.1007/BF01058439

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 Hamiltonian H(phi), absence of critical slowing down can only be expected if the expansion of in terms of the shift psi contains no relevant (mass) term. We also introduce a multigrid update procedure for nonabelian lattice gauge theory and study the acceptance rates for gauge group SU(2) in four dimensions.

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