Wilsonian Approximated Renormalization Group for Matrix and Vector Models in 2<d<4

Abstract

Wilson's approximation scheme of RG recursion formula dropping momentum dependence of the propagators is applied to large-$N$ vector and matrix models in dimensions $2<d<4$ by making use of their exact solutions in zero dimension. In spite of apparent dependence of critical exponents upon the dilatational parameter $\rho$ involved by the approximation, the exact exponents are reproduced for vector models in the limit $\rho\rightarrow 0$. Application to matrix models is then reexamined after the same fashion. It predicts critical exponents $\nu=2/d$ and $\eta=2-d/2$ for the $\tr \Phi^4$ matrix model.