  In the limit where $N\to\infty$ and the coupling constant $g \to g_{c}$ in a
correlated manner, O(N) symmetric vector models represent filamentary surfaces.
The purpose of these studies is to gain intuition for the long lasting search
for a possible description of quantum field theory in terms of extended
objects. It is shown here that a certain limiting procedure has to be followed
in order to avoid several difficulties in establishing the theory at a critical
negative coupling constant. It is also argued that at finite temperature a
certain metastable-false vacuum disappears as the temperature is increased.
