Multigrid Monte Carlo in the Sine Gordon model

TL;DR

This paper investigates the effectiveness of multigrid Monte Carlo methods in the 2D Sine Gordon model, finding that while critical slowing down occurs, increasing updates on coarser lattices does not mitigate it.

Contribution

It provides an empirical analysis of multigrid Monte Carlo performance in the Sine Gordon model, highlighting limitations in reducing critical slowing down.

Findings

Critical slowing down occurs in the model.

Increasing coarser lattice updates does not reduce slowing down.

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.