Multigrid Monte Carlo method. IV. One-dimensional O(4)-symmetric nonlinear σ model

We study the dynamic critical behavior of the multigrid Monte Carlo algorithm with piecewise-constant interpolation and a W cycle, applied to the one-dimensional O(4)-symmetric nonlinear σ model [=SU(2) principal chiral model], on lattices from L=128 to L=16 384. Our data for the integrated autocorrelation time ${\mathrm{\tau }}_{\mathrm{i}\mathrm{n}\mathrm{t},{\mathcal{M}}^2}$ are well fit by a logarithmic growth. We have no idea why the critical slowing-down is not completely eliminated. © 1996 The American Physical Society.