  An approximation formula is derived for acceptance rates of nonlocal
Metropolis updates in simulations of lattice field theories. The predictions of
the formula agree quite well with Monte Carlo simulations of 2-dimensional Sine
Gordon, XY and phi**4 models. The results are consistent with the following
rule: For a critical model with a fundamental Hamiltonian H(phi) sufficiently
high acceptance rates for a complete elimination of critical slowing down can
only be expected if the expansion of < H(phi+psi) > in terms of the shift psi
contains no relevant term (mass term).
