Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
2009-05-12
Nucl.Phys.B824:563-615,2010
Physics
High Energy Physics
High Energy Physics - Lattice
62 pages, 15 figures, published version with references added
Scientific paper
10.1016/j.nuclphysb.2009.09.007
Lattice artifacts in the 2d O(n) non-linear sigma-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 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(a))^3, 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.
Balog Janos
Niedermayer Ferenc
Weisz Peter
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