  Recent interest in large N matrix models in the double scaling limit raised
new interest also in O(N) vector models. The limit $N \rightarrow \infty$,
correlated with the limit $g \rightarrow g_c$, results in an expansion in terms
of filamentary surfaces and explicit calculations can be carried out also in
dimensions $d\geq 2$. It is shown here that the absence of physical massless
bound states in two dimensions sets strong constraints on this limit.
