  We explore the implications of recent work by Br\'ezin and Zinn-Justin,
applying the renormalization group techniques from critical phenomena to the
scaling limit of matrix models in two-dimensional quantum gravity. They
endeavor to get the lowest order fixed points of the theory giving insight upon
the critical points of the theory. We show that at leading order the
perturbative result is equal to the saddle-point approximation result. We
calculate the next-to-leading order in the perturbative expansion exploring the
goodness of the approach.
