The fate of the Wilson-Fisher fixed point in non-commutative ϕ4

Abstract

In this article we study non-commutative vector sigma model with the most general ϕ4 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.