Multigrid Monte Carlo with higher cycles in the Sine Gordon model

TL;DR

This paper investigates whether higher cycle multigrid Monte Carlo methods can reduce critical slowing down in the 2D Sine Gordon model, finding that increasing work on coarser lattices does not improve performance.

Contribution

The study evaluates the effectiveness of higher cycle multigrid Monte Carlo in mitigating critical slowing down in the Sine Gordon model, showing no improvement with increased cycles.

Findings

Higher cycle (gamma=4) does not reduce critical slowing down.

Increasing work on coarser lattices does not improve acceptance rates.

Multigrid methods with higher cycles are ineffective for this model.

Abstract

We study the dynamical critical behavior of multigrid Monte Carlo for the two dimensional Sine Gordon model on lattices up to 128 x 128. Using piecewise constant interpolation, we perform a W-cycle (gamma=2). We examine whether one can reduce critical slowing down caused by decreasing acceptance rates on large blocks by doing more work on coarser lattices. To this end, we choose a higher cycle with gamma = 4. The results clearly demonstrate that critical slowing down is not reduced in either case.