  In this article we study non-commutative vector sigma model with the most
general \phi^4 interaction on Moyal-Weyl spaces. We compute the 2- and 4-point
functions to all orders in the large N limit and then apply the approximate
Wilson renormalization group recursion formula to study the renormalized
coupling constants of the theory. The non-commutative Wilson-Fisher fixed point
interpolates between the commutative Wilson-Fisher fixed point of the Ising
universality class which is found to lie at zero value of the critical coupling
constant a_* of the zero dimensional reduction of the theory, and a novel
strongly interacting fixed point which lies at infinite value of a_*
corresponding to maximal non-commutativity beyond which the two-sheeted
structure of a_* as a function of the dilation parameter disappears.
