Institut füt;r Theoretische Physik

Universität;t Hamburg

Luruper Chaussee 149

D-2000 Hamburg 50, Germany

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

Contributed July 28, 1992.