Logarithmic corrections to O(a2) lattice artifacts

We compute logarithmic corrections to the O(a2) lattice artifacts for a class of lattice actions for the non-linear O(n) sigma-model in two dimensions. The generic leading artifacts are of the form a2[ln(a2)]n/(n−2). We also compute the next-to-leading corrections and show that for the case n=3 the resulting expressions describe well the lattice artifacts in the step scaling function, which are in a large range of the cutoff apparently of the form O(a). An analogous computation should, if technically possible, accompany any precision measurements in lattice QCD.