Acceptance Rates in Multigrid Monte Carlo

TL;DR

This paper derives an approximation formula for acceptance rates in multigrid Monte Carlo methods and validates it against simulations of various 2D lattice models, highlighting conditions to eliminate critical slowing down.

Contribution

It introduces a new approximation formula for acceptance rates in nonlocal Metropolis updates and demonstrates its accuracy across multiple lattice models.

Findings

The formula agrees well with Monte Carlo simulations.

High acceptance rates can eliminate critical slowing down if the Hamiltonian expansion lacks relevant mass terms.

The results support a rule linking acceptance rates to the presence of relevant terms in the Hamiltonian expansion.

Abstract

An approximation formula is derived for acceptance rates of nonlocal Metropolis updates in simulations of lattice field theories. The predictions of the formula agree quite well with Monte Carlo simulations of 2-dimensional Sine Gordon, XY and phi**4 models. The results are consistent with the following rule: For a critical model with a fundamental Hamiltonian H(phi) sufficiently high acceptance rates for a complete elimination of critical slowing down can only be expected if the expansion of < H(phi+psi) > in terms of the shift psi contains no relevant term (mass term).