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The Wilsonian renormalization group approach to matrix models is outlined and applied to multitrace matrix models with emphasis on the computation of the fixed points which could describe the phase structure of noncommutative scalar phi-four theory., Comment: The review section of the RG method for matrix models is replaced with a brief discussion of the fixed points of the cubic-quartic matrix model. The main contribution regarding the multitrace cubic matrix model is left intact. In summary, we employ a consistent mean-field approximation in which Tr M/N is replaced by its expectation value a_1=

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

In this article we exhibit explicitly the matrix model ($\theta=\infty$) fixed point of phi-four theory on noncommutative spacetime with only two noncommuting directions using the Wilson renormalization group recursion formula and the 1/N expansion of the zero dimensional reduction and then calculate the mass critical exponent $\nu$ and the anomalous dimension $\eta$ in various dimensions ., Comment: v3: 51 pages, section 3 is enlarged further, section 6 on the Grosse-Vignes-Tourneret model is new, a new appendix is added, the rest is unchanged