Wilson RG of Noncommutative $Φ_{4}^4$

We present a study of phi-four theory on noncommutative spaces using a combination of the Wilson renormalization group recursion formula and the solution to the zero dimensional vector/matrix models at large $N$. Three fixed points are identified. The matrix model $θ=\infty$ fixed point which describes the disordered-to-non-uniform-ordered transition. The Wilson-Fisher fixed point at $θ=0$ which describes the disordered-to-uniform-ordered transition, and a noncommutative Wilson-Fisher fixed point at a maximum value of $θ$ which is associated with the transition between non-uniform-order and uniform-order phases.

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