### Abstract

We study a class of Monte Carlo algorithms for the nonlinear σ-model, based on a Wolff-type embedding of Ising spins into the target manifold M. We argue heuristically that such an algorithm can have dynamic critical exponent z ≪ 2 only if the embedding is based on an involutive isometry of M whose fixed-point manifold has codimension 1. Such an isometry exists only if the manifold is a product of spheres and discrete quotients of spheres. Numerical simulations of the codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield z = 1.5 ± 0.3, in agreement with our heuristic argument.

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

Pages (from-to) | 72-75 |

Number of pages | 4 |

Journal | Nuclear Physics B - Proceedings Supplements |

Volume | 20 |

Issue number | C |

DOIs | |

State | Published - May 20 1991 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B - Proceedings Supplements*,

*20*(C), 72-75. https://doi.org/10.1016/0920-5632(91)90883-G

**Generalized Wolff-type embedding algorithms for nonlinear σ-models.** / Caracciolo, Sergio; Edwards, Robert G.; Pelissetto, Andrea; Sokal, Alan D.

Research output: Contribution to journal › Article

*Nuclear Physics B - Proceedings Supplements*, vol. 20, no. C, pp. 72-75. https://doi.org/10.1016/0920-5632(91)90883-G

}

TY - JOUR

T1 - Generalized Wolff-type embedding algorithms for nonlinear σ-models

AU - Caracciolo, Sergio

AU - Edwards, Robert G.

AU - Pelissetto, Andrea

AU - Sokal, Alan D.

PY - 1991/5/20

Y1 - 1991/5/20

N2 - We study a class of Monte Carlo algorithms for the nonlinear σ-model, based on a Wolff-type embedding of Ising spins into the target manifold M. We argue heuristically that such an algorithm can have dynamic critical exponent z ≪ 2 only if the embedding is based on an involutive isometry of M whose fixed-point manifold has codimension 1. Such an isometry exists only if the manifold is a product of spheres and discrete quotients of spheres. Numerical simulations of the codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield z = 1.5 ± 0.3, in agreement with our heuristic argument.

AB - We study a class of Monte Carlo algorithms for the nonlinear σ-model, based on a Wolff-type embedding of Ising spins into the target manifold M. We argue heuristically that such an algorithm can have dynamic critical exponent z ≪ 2 only if the embedding is based on an involutive isometry of M whose fixed-point manifold has codimension 1. Such an isometry exists only if the manifold is a product of spheres and discrete quotients of spheres. Numerical simulations of the codimension-2 algorithm for the two-dimensional O(4)-symmetric σ-model yield z = 1.5 ± 0.3, in agreement with our heuristic argument.

UR - http://www.scopus.com/inward/record.url?scp=4243881248&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243881248&partnerID=8YFLogxK

U2 - 10.1016/0920-5632(91)90883-G

DO - 10.1016/0920-5632(91)90883-G

M3 - Article

AN - SCOPUS:4243881248

VL - 20

SP - 72

EP - 75

JO - Nuclear and Particle Physics Proceedings

JF - Nuclear and Particle Physics Proceedings

SN - 2405-6014

IS - C

ER -