Wilson RG of Noncommutative ${\Phi }_4^4$

Abstract

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 $\theta =\infty$ fixed point which describes the disordered-to-non-uniform-ordered transition. The Wilson-Fisher fixed point at $\theta =0$ which describes the disordered-to-uniform-ordered transition, and a noncommutative Wilson-Fisher fixed point at a maximum value of $\theta$ which is associated with the transition between non-uniform-order and uniform-order phases.

Comments: 28 pages, one table, 8 figures. arXiv admin note: substantial text overlap with arXiv:1304.7303