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Physical review. B, Condensed matter

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

Daniel Kandel, Eytan Domany, Achi Brandt

Published Jul 1, 1989• 66 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.40.330

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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.
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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.