Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Multigrid Monte Carlo in the Sine Gordon model

Grabenstein, M, Mikeska, B

Published Nov 18, 1993• 3 citations
OpenAlex

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.

Related papers

Suppressing critical slowing down in two-dimensional Ising model simulations by the multigrid Monte Carlo method

E. Stoll

Statistically independent equilibrium configurations of interacting systems can easily be generated with little computing effort by multigrid coarse-to-fine transforms. The very slow long-wavelength motions close to critical points are thereby accelerated by many orders of magnitude. This is demonstrated with a novel updating algorithm from small to large two-dimensional Ising systems specifying effective interactions according to renormalisation group considerations, corrected for non-linearities and saturation effects.

Journal of Physics Condensed Matter•Oct 2, 1989•8 citations

Simulations without critical slowing down

Daniel Kandel, Eytan Domany, Dorit Ron +2 more

We have developed a novel simulation method that combines a multigrid technique with a stochastic blocking procedure. Our algorithm eliminates critical slowing down completely, as demonstrated by simulations of the two-dimensional Ising model at criticality.

Physical Review Letters•Apr 18, 1988•97 citations

Multiscale Monte Carlo Algorithms in Statistical Mechanics and Quantum Field Theory

P.G. Lauwers

Conventional Monte Carlo simulation algorithms for models in statistical mechanics and quantum field theory are afflicted by problems caused by their locality. They become highly inefficient if investigations of critical or nearly-critical systems, i.e., systems with important large scale phenomena, are undertaken. We present two types of multiscale approaches that alleveate problems of this kind: stochastic cluster algorithms and multigrid Monte Carlo simulation algorithms. Another formidable computational problem in simulations of phenomenologically relevant field theories with fermions is the need for frequently inverting the Dirac operator. This inversion can be accelerated considerably by means of deterministic multigrid methods, very similar to the ones used for the numerical solution of differential equations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Birkhäuser Basel eBooks•Jan 1, 1991•2 citations

Simulations without critical slowing down: Ising and three-state Potts models

Daniel Kandel, Eytan Domany, Achi Brandt

We have developed a novel simulation method that combines a multigrid technique with a stochastic blocking procedure. Our algorithm eliminates critical slowing down completely, as we demonstrated previously by simulating the two-dimensional Ising model at criticality. Here we describe results of much more extensive simulations of the two-dimensional Ising and three-state Potts models and provide a heuristic argument to explain why our method works.

Physical review. B, Condensed matter•Jul 1, 1989•66 citations

LATTICE SPIN MODELS AND NEW ALGORITHMS — A REVIEW OF MONTE CARLO COMPUTER SIMULATIONS

CLIVE F. BAILLIE

We review Monte Carlo computer simulations of spin models — both discrete and continuous. We explain the phenomenon of critical slowing which seriously degrades the efficiency of standard local Monte Carlo algorithms such as the Metropolis algorithm near phase transitions. We then go onto describe in detail the new algorithms which ameliorate the problem of critical slowing down, and give their dynamical critical exponent values.

International Journal of Modern Physics C•Apr 1, 1990•27 citations

Multigrid Monte Carlo Simulations

Fung-kiu Chow, P. Kevin MacKeown

With a view to eventually studying quantum effects in the thermal behaviour of Lennard-Jones clusters, we investigate the extent to which the limitations of quasi-ergodicity and critical slowing down can be overcome in the evaluation of imaginary time path integrals using the Multigrid method. We show the power of the method by looking at the correlation times for a 2 Ar atom Lennard Jones cluster along the lines described in Janke & Sauer's paper.1)

Progress of Theoretical Physics Supplement•Jan 1, 2000•0 citations
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.
Statistically independent equilibrium configurations of interacting systems can easily be generated with little computing effort by multigrid coarse-to-fine transforms. The very slow long-wavelength motions close to critical points are thereby accelerated by many orders of magnitude. This is demonstrated with a novel updating algorithm from small to large two-dimensional Ising systems specifying effective interactions according to renormalisation group considerations, corrected for non-linearities and saturation effects.
Conventional Monte Carlo simulation algorithms for models in statistical mechanics and quantum field theory are afflicted by problems caused by their locality. They become highly inefficient if investigations of critical or nearly-critical systems, i.e., systems with important large scale phenomena, are undertaken. We present two types of multiscale approaches that alleveate problems of this kind: stochastic cluster algorithms and multigrid Monte Carlo simulation algorithms. Another formidable computational problem in simulations of phenomenologically relevant field theories with fermions is the need for frequently inverting the Dirac operator. This inversion can be accelerated considerably by means of deterministic multigrid methods, very similar to the ones used for the numerical solution of differential equations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.