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

J. Balog, Ferenc Niedermayer, Peter Weisz

Research output: Contribution to journalArticle

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Abstract

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.

Original languageEnglish
Pages (from-to)563-615
Number of pages53
JournalNuclear Physics B
Volume824
Issue number3
DOIs
Publication statusPublished - Jan 11 2010

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

In: Nuclear Physics B, Vol. 824, No. 3, 11.01.2010, p. 563-615.

Research output: Contribution to journalArticle

Balog, J. ; Niedermayer, Ferenc ; Weisz, Peter. / The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution. In: Nuclear Physics B. 2010 ; Vol. 824, No. 3. pp. 563-615.
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