  We suggest that the $\phi^4$ model is only a polynomial approximation to a
more fundamental theory. As a consequence the high temperature regime might not
be correctly described by this model. If this turns out to be true then several
results concerning e.g., critical temperatures, symmetry restoration at high
temperature and high temperature expansions should be reconsidered. We
illustrate our conjecture by using the Nambu-Goto string model. We compare a
two-loop calculation of the free energy or quark-antiquark static potential at
finite temperature with a previous exact calculation in the large-d limit and
show how the perturbative expansion fails to reproduce important features in
the neighborhood of the critical temperature. It becomes clear why this happens
in the Nambu-Goto model and we suggest that perhaps something similar occurs
with the $\phi^4$ model.
