Theoretical Analysis of Acceptance Rates in Multigrid Monte Carlo

TL;DR

This paper provides a theoretical framework for analyzing acceptance rates in multigrid Monte Carlo algorithms, helping to predict their effectiveness in overcoming critical slowing down in complex models.

Contribution

It introduces a criterion for assessing multigrid algorithm efficiency and applies it to spin models and nonabelian lattice gauge theories.

Findings

Criterion predicts multigrid success in spin models

Detailed kinematic analysis of gauge theory algorithm

Guidelines for overcoming critical slowing down

Abstract

We analyze the kinematics of multigrid Monte Carlo algorithms by investigating acceptance rates for nonlocal Metropolis updates. With the help of a simple criterion we can decide whether or not a multigrid algorithm will have a chance to overcome critial slowing down for a given model. Our method is introduced in the context of spin models. A multigrid Monte Carlo procedure for nonabelian lattice gauge theory is described, and its kinematics is analyzed in detail.