Multigrid acceleration for asymptotically free theories.
We present a multigrid Monte Carlo algorithm with piecewise-linear interpolation operator for nonlinear {sigma} models with global chiral SU({ital N}){times}SU({ital N}) symmetry or CP{sup {ital N}{minus}1} manifold. We demonstrate its efficiency in the two-dimensional SU(3){times}SU(3) chiral model and the CP{sup 3} nonlinear {sigma} model for correlation length up to 77 in lattice units. On lattices up to size 512{times}512 we achieve almost complete elimination of critical slowing down in the CP{sup 3} case, with a dynamical critical exponent {ital z}{sub MGMC}=0.2{plus minus}0.1. Asymptotic scaling with the bare coupling does not appear to set in for the standard action of both models in the range of parameters studied.