Multigrid Monte Carlo in the Sine Gordon model

Abstract

We pose two questions about the dynamical critical behavior of multigrid Monte Carlo: Will a multigrid Monte Carlo simulation of the two dimensional Sine Gordon model exhibit critical slowing down, as expected by a theoretical analysis of Metropolis acceptance rates? Can we reduce critical slowing down caused by decreasing acceptance rates on large blocks by performing more updates on coarser lattices? To this end we simulate the model with a W-cycle (gamma = 2) and a higher cycle with gamma = 4 using piecewise constant interpolation. The answer to the first question is positive, the answer to the second one is negative.