High temperature critical O(N) field models by LCE series

The critical properties of renormalizable O(N) field models are determined by means of the high order (≥ 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 three-dimensional models. Concerning critical amplitudes and subcritical behaviour, corrections induced by renormalizable couplings are measurable.