Multigrid Monte Carlo Method for Lattice Field Theories

Abstract

We propose a stochastic generalization of the multigrid method, which reduces critical slowing down in Monte Carlo computations of lattice field theories. For free fields, critical slowing down is completely eliminated. For a ${\ensuremath{\varphi}}^{4}$ model, numerical experiments show a factor of \ensuremath{\cong} 10 reduction, over a standard heat-bath algorithm, in the work needed to get a given accuracy (error-bar size).