Kinematics of Multigrid Monte Carlo

M. Grabenstein
Institut füt;r Theoretische Physik
Universität;t Hamburg
Luruper Chaussee 149
D-2000 Hamburg 50, Germany

K. Pinn
Institut füt;r Theoretische Physik I
Universität;t Müt;nster
Wilhelm-Klemm-Str. 9
D-4400 Müt;nster, Germany


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.

Contributed July 28, 1992.