### 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 |
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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 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics B*,

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