  We introduce a field-theoretic approach for describing the critical behavior
of nonextensive systems, systems displaying global correlations among their
degrees of freedom, encoded by the nonextensive parameter $q$. As some
applications, we report, to our knowledge, the first analytical computation of
both universal static and dynamic $q$-dependent nonextensive critical exponents
for O($N$) vector models, valid for all loop orders and $|q - 1| < 1$. Then
emerges the new nonextensive O($N$)$_{q}$ universality class. We employ six
independent methods which furnish identical results. Particularly, the results
for nonextensive 2d Ising systems, exact within the referred approximation,
agree with that obtained from computer simulations, within the margin of error,
as better as $q$ is closer to $1$. We argue that the present approach can be
applied to all models described by extensive statistical field theory as well.
The results show an interplay between global correlations and fluctuations.
