The puzzle of apparent linear lattice artifacts in the 2d non-linear sigma-model and Symanzik's solution
Abstract:
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 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. (c) 2009 Elsevier B.V. All rights reserved.