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

Janos Balog, Ferenc Niedermayer, Peter Weisz

Research output: Contribution to journalArticle

21 Citations (Scopus)

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

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

Fingerprint Dive into the research topics of 'The puzzle of apparent linear lattice artifacts in the 2d non-linear σ-model and Symanzik's solution'. Together they form a unique fingerprint.

  • Cite this