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

TL;DR

This paper applies Wilson's approximation scheme to large-N vector and matrix models in dimensions between 2 and 4, successfully reproducing exact critical exponents for vector models and predicting new exponents for matrix models.

Contribution

The study extends Wilson's approximation to large-N vector and matrix models in 2<d<4, deriving critical exponents and providing new predictions for matrix models.

Findings

Exact exponents for vector models are reproduced in the limit 

Predicted critical exponents for matrix models: =2/d, =2-d/2

Application of the approximation scheme to matrix models yields new critical exponent predictions.

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.