  We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC)
algorithm with piecewise-constant interpolation applied to the two-dimensional
O(4)-symmetric nonlinear $\sigma$-model [= SU(2) principal chiral model], on
lattices up to $256 \times 256$. We find a dynamic critical exponent
$z_{int,{\cal M}^2} = 0.60 \pm 0.07$ for the W-cycle and $z_{int,{\cal M}^2} =
1.13 \pm 0.11$ for the V-cycle, compared to $z_{int,{\cal M}^2} = 2.0 \pm 0.15$
for the single-site heat-bath algorithm (subjective 68% confidence intervals).
Thus, for this asymptotically free model, critical slowing-down is greatly
reduced compared to local algorithms, but not completely eliminated. For a $256
\times 256$ lattice, W-cycle MGMC is about 35 times as efficient as a
single-site heat-bath algorithm.
