  Recently it has been claimed that ordinary perturbation theory (OPT) gives
incorrect weak coupling expansions for lattice O(N) non-linear sigma models in
the infinite volume limit, and in particular that the two-dimensional
non-abelian models are not asymptotically free, contrary to previous findings.
Here it is argued that the problem occurs only for one-dimensional infinite
lattices, and that in general, OPT gives correct expansions if physical
quantities are first computed on a finite lattice, and the infinite volume
limit is taken at the end. In one dimension the expansion is sensitive to
boundary conditions because of the severe infrared behavior, but this is not
expected to happen in higher dimensions. It is concluded that spin
configurations which are far from the perturbative vacuum have too small a
measure in the path integral to invalidate OPT, even though they are
energetically allowed for non-zero values of the coupling.
