### Abstract

We introduce a new and very convenient approach to multi-grid Monte Carlo (MGMC) algorithms for general nonlinear σ-models: it is based on embedding an XY model into the given σ-model, and then updating the induced XY model using a standard XY-model MGMC code. We study the dynamic critical behavior of this algorithm for the two-dimensional O(N) σ-models with N = 3,4,8 and for the SU(3) principal chiral model. We find that the dynamic critical exponent z varies systematically between these different asymptotically free models: it is approximately 0.70 for O(3), 0.60 for O(4), 0.50 for O(8), and 0.45 for SU(3). It goes without saying that we have no theoretical explanation of this behavior.

Original language | English (US) |
---|---|

Pages (from-to) | 796-799 |

Number of pages | 4 |

Journal | Nuclear Physics B - Proceedings Supplements |

Volume | 47 |

Issue number | 1-3 |

DOIs | |

State | Published - Mar 1996 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B - Proceedings Supplements*,

*47*(1-3), 796-799. https://doi.org/10.1016/0920-5632(96)00177-6

**Dynamic critical behavior of multi-grid Monte Carlo for two-dimensional nonlinear σ-models.** / Mana, Gustavo; Mendes, Tereza; Pelissetto, Andrea; Sokal, Alan D.

Research output: Contribution to journal › Article

*Nuclear Physics B - Proceedings Supplements*, vol. 47, no. 1-3, pp. 796-799. https://doi.org/10.1016/0920-5632(96)00177-6

}

TY - JOUR

T1 - Dynamic critical behavior of multi-grid Monte Carlo for two-dimensional nonlinear σ-models

AU - Mana, Gustavo

AU - Mendes, Tereza

AU - Pelissetto, Andrea

AU - Sokal, Alan D.

PY - 1996/3

Y1 - 1996/3

N2 - We introduce a new and very convenient approach to multi-grid Monte Carlo (MGMC) algorithms for general nonlinear σ-models: it is based on embedding an XY model into the given σ-model, and then updating the induced XY model using a standard XY-model MGMC code. We study the dynamic critical behavior of this algorithm for the two-dimensional O(N) σ-models with N = 3,4,8 and for the SU(3) principal chiral model. We find that the dynamic critical exponent z varies systematically between these different asymptotically free models: it is approximately 0.70 for O(3), 0.60 for O(4), 0.50 for O(8), and 0.45 for SU(3). It goes without saying that we have no theoretical explanation of this behavior.

AB - We introduce a new and very convenient approach to multi-grid Monte Carlo (MGMC) algorithms for general nonlinear σ-models: it is based on embedding an XY model into the given σ-model, and then updating the induced XY model using a standard XY-model MGMC code. We study the dynamic critical behavior of this algorithm for the two-dimensional O(N) σ-models with N = 3,4,8 and for the SU(3) principal chiral model. We find that the dynamic critical exponent z varies systematically between these different asymptotically free models: it is approximately 0.70 for O(3), 0.60 for O(4), 0.50 for O(8), and 0.45 for SU(3). It goes without saying that we have no theoretical explanation of this behavior.

UR - http://www.scopus.com/inward/record.url?scp=16144367785&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=16144367785&partnerID=8YFLogxK

U2 - 10.1016/0920-5632(96)00177-6

DO - 10.1016/0920-5632(96)00177-6

M3 - Article

VL - 47

SP - 796

EP - 799

JO - Nuclear and Particle Physics Proceedings

JF - Nuclear and Particle Physics Proceedings

SN - 2405-6014

IS - 1-3

ER -