Kinematics of Multigrid Monte Carlo

Abstract

We study the kinematics of multigrid Monte Carlo algorithms by means of acceptance rates for nonlocal Metropolis update proposals. An approximation formula for acceptance rates is derived. We present a comparison of different coarse-to-fine interpolation schemes in free field theory, where the formula is exact. The predictions of the approximation formula for several interacting models are well confirmed by Monte Carlo simulations. The following rule is found: For a critical model with fundamental Hamiltonian H(phi), absence of critical slowing down can only be expected if the expansion of <H(phi + psi)> in terms of the shift psi contains no relevant (mass) term. We also introduce a multigrid update procedure for nonabelian lattice gauge theory and study the acceptance rates for gauge group SU(2) in four dimensions.

28 pages, 8 ps-figures, DESY 92-094

References in corpus (4)

• Multi-Grid Monte Carlo III. Two-Dimensional O(4)-Symmetric Nonlinear $\sigma$-Model
• Multigrid Methods in Lattice Field Computations
• Acceptance Rates in Multigrid Monte Carlo
• High Precision Verification of the Kosterlitz Thouless Scenario

Cited by in corpus (7)

• Application of Multicanonical Multigrid Monte Carlo Method to the Two-Dimensional ${\varphi }^4$-Model: Autocorrelations and Interface Tension
• Multi-Grid Monte Carlo via $XY$ Embedding. II. Two-Dimensional $SU(3)$ Principal Chiral Model
• Multi-Grid Monte Carlo via $XY$ Embedding I. General Theory and Two-Dimensional $O(N)$-Symmetric Nonlinear $\sigma$-Models
• Progress in Lattice Field Theory Algorithms
• Multigrid Monte Carlo Algorithms for SU(2) Lattice Gauge Theory: Two versus Four Dimensions
• Multi-Grid Monte Carlo. IV. One-Dimensional $O(4)$-Symmetric Nonlinear $\sigma$-Model
• Multigrid Monte Carlo in the Sine Gordon model