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arXiv · 1206.5653

The fate of the Wilson-Fisher fixed point in non-commutative \phi^4

Badis Ydri·Adel Bouchareb
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Abstract

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.

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Badis Ydri, Adel Bouchareb. 2012-06-25. The fate of the Wilson-Fisher fixed point in non-commutative \phi^4. https://doi.org/10.1063/1.4754816

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