MULTIGRID MONTE-CARLO .3. 2-DIMENSIONAL O(4)-SYMMETRICAL NONLINEAR SIGMA-MODEL

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 non-linear sigma-model [= SU(2) principal chiral model], on lattices up to 256x256. We find a dynamic critical exponent z(int,M2) = 0.60+/-0.07 for the W-cycle and z(int,M2) = 1.13+/-0.11 for the V-cycle, compared to z(int,M2) = 2.0+/-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 256x256 lattice, W-cycle MGMC is about 35 times as efficient as a single-site heat-bath algorithm.