Wilsonian approximated renormalization group for matrix and vector models in 2 < d < 4

Abstract

Wilson's approximation scheme of RG recursion formula is applied to large- N vector and matrix models in dimensions 2 < d < 4 by making use of their exact solutions in zero dimension. Apparent nonuniversality is present in higher order terms of the ϵ-expansion under this approximation, and is shown to be removed in a certain limit to yield an exact exponent for vector models. Application to matrix models, considered previously by Ferretti, is then reexamined in this limit. It predicts critical exponents ν = 2 d and η = 2 − d 2 for the tr Φ 4 matrix model in 2 < d < 4.