  We investigate a vectorial O(N) model with a generic nearest-neighbor
interaction W(\bsigma_i\cdot \bsigma_j) (depending on {\cal N} tunable
parameters), a Yukawa (and Gross Neveu) model with N_f fermions at finite
temperature and the vectorial \phi^6 model, in the large N (N_f) limit. All
this models exhibit a Mean Field critical point for N=\infinity. When 1/N
fluctuations are included, infra red divergences appear near the critical
point. In the framework of a generalized 1/N expansion we show that these
divergences are related to a universal crossover mechanism between the Mean
Field universality class (N=\infinity) and the nonclassical one for
N<\infinity. For the generic nearest-neighbor interaction multicritical points
are also investigated.
