### Abstract

Lattice artifacts in the 2d O(n) non-linear σ-model are expected to be of the form O (a^{2}), and hence it was (when first observed) disturbing that some quantities in the O (3) model with various actions show parametrically stronger cutoff dependence, apparently O (a), up to very large correlation lengths. In a previous letter Balog et al. (2009) [1] we described the solution to this puzzle. Based on the conventional framework of Symanzik's effective action, we showed that there are logarithmic corrections to the O (a^{2}) artifacts which are especially large (ln^{3} a) for n = 3 and that such artifacts are consistent with the data. In this paper we supply the technical details of this computation. Results of Monte Carlo simulations using various lattice actions for O (3) and O (4) are also presented.

Original language | English |
---|---|

Pages (from-to) | 563-615 |

Number of pages | 53 |

Journal | Nuclear Physics B |

Volume | 824 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 11 2010 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics B*,

*824*(3), 563-615. https://doi.org/10.1016/j.nuclphysb.2009.09.007

**The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution.** / Balog, J.; Niedermayer, Ferenc; Weisz, Peter.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 824, no. 3, pp. 563-615. https://doi.org/10.1016/j.nuclphysb.2009.09.007

}

TY - JOUR

T1 - The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution

AU - Balog, J.

AU - Niedermayer, Ferenc

AU - Weisz, Peter

PY - 2010/1/11

Y1 - 2010/1/11

N2 - Lattice artifacts in the 2d O(n) non-linear σ-model are expected to be of the form O (a2), and hence it was (when first observed) disturbing that some quantities in the O (3) model with various actions show parametrically stronger cutoff dependence, apparently O (a), up to very large correlation lengths. In a previous letter Balog et al. (2009) [1] we described the solution to this puzzle. Based on the conventional framework of Symanzik's effective action, we showed that there are logarithmic corrections to the O (a2) artifacts which are especially large (ln3 a) for n = 3 and that such artifacts are consistent with the data. In this paper we supply the technical details of this computation. Results of Monte Carlo simulations using various lattice actions for O (3) and O (4) are also presented.

AB - Lattice artifacts in the 2d O(n) non-linear σ-model are expected to be of the form O (a2), and hence it was (when first observed) disturbing that some quantities in the O (3) model with various actions show parametrically stronger cutoff dependence, apparently O (a), up to very large correlation lengths. In a previous letter Balog et al. (2009) [1] we described the solution to this puzzle. Based on the conventional framework of Symanzik's effective action, we showed that there are logarithmic corrections to the O (a2) artifacts which are especially large (ln3 a) for n = 3 and that such artifacts are consistent with the data. In this paper we supply the technical details of this computation. Results of Monte Carlo simulations using various lattice actions for O (3) and O (4) are also presented.

UR - http://www.scopus.com/inward/record.url?scp=74449086526&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=74449086526&partnerID=8YFLogxK

U2 - 10.1016/j.nuclphysb.2009.09.007

DO - 10.1016/j.nuclphysb.2009.09.007

M3 - Article

AN - SCOPUS:74449086526

VL - 824

SP - 563

EP - 615

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -