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Lattice artifacts in the 2d O(n) non-linear sigma-model are expected to be ofthe form O(a^2), and hence it was (when first observed) disturbing that somequantities in the O(3) model with various actions show parametrically strongercutoff dependence, apparently O(a), up to very large correlation lengths. In aprevious letter we described the solution to this puzzle. Based on theconventional framework of Symanzik's effective action, we showed that there arelogarithmic 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. Inthis paper we supply the technical details of this computation. Results ofMonte Carlo simulations using various lattice actions for O(3) and O(4) arealso presented.

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