### Abstract

We study the dynamic critical behavior of the multi-grid Monte Carlo (MGMC) algorithm with piecewise-constant interpolation applied to the two-dimensional O(4)-symmetric non-linear σ-model [ = SU(2) principal chirral model]], on lattices up to 256×256. We find a dynamic critical exponent z_{int,M2} = 0.60±0.07 for the W-cycle and z_{int,M2 = 1.13±0.11} for the V-cycle, compared to z_{int,M2} = 2.0±0.15 for the single-site heat-bath algorithm (subjective 68% confidence intervals). Thus, for this asymptotically free model, critical slowing-down is greatly reduced compared to local algorithms, but not completely eliminated. For a 256×256 lattice, W-cycle MGMC is about 35 times as efficient as a single-site heat-bath algorithm.

Original language | English (US) |
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Pages (from-to) | 621-664 |

Number of pages | 44 |

Journal | Nuclear Physics, Section B |

Volume | 380 |

Issue number | 3 |

DOIs | |

State | Published - Aug 10 1992 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*380*(3), 621-664. https://doi.org/10.1016/0550-3213(92)90262-A