  The critical properties of renormalizable O(N) field models are determined by
means of the high order ($\geq 18$) behaviour of convergent linked cluster
series on finite temperature lattices. It is shown that those models become
weakly coupled at the phase transition. The critical exponents agree to those
of the corresponding superrenormalizable 3-dimensional models. Concerning
critical amplitudes and subcritical behaviour, corrections induced by
renormalizable couplings are measurable.
