  We point out that the $1/N$ expansion, which is widely invoked to infer
properties of the $2D$ $O(N)$ models, is nonuniform in the temperature, i.e.
with decreasing temperature the $1/N$ expansion truncated at a fixed order
deviates more and more from the true answer. This fact precludes the use of the
expansion to deduce low temperature properties such as asymptotic scaling for
those models. By contrast, in the $1D$ $O(N)$ chains, there are no signs of
such a nonuniformity.
