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.
We describe a novel simulation method that eliminates the slowing-down problem in the Monte Carlo (MC) simulations of imaginary-time path integrals near the continuum limit. This method combines a stochastic blocking procedure with the multigrid method to rapidly accelerate the sampling of paths in a quantum MC simulation, making its dynamics more ergodic. The effectiveness and efficiency of this method are demonstrated for several one-dimensional quantum systems and compared to other standard and accelerated methods.
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.