Higher Order Calculations in Renormalization Group Approach to Matrix Models

TL;DR

This paper advances the renormalization group analysis of matrix models by computing higher order approximations, demonstrating convergence of fixed points and critical exponents towards exact solutions.

Contribution

It introduces higher order approximation techniques in the RG approach to matrix models and shows their effectiveness in approaching exact results.

Findings

Fixed point values converge with higher order approximations.

String susceptibility exponent approaches the exact value.

Effective beta function computed up to fifth order.

Abstract

We study higher order approximations in the renormalization group approach to matrix models. We use constraint equations on the free energy resulting from a freedom of field redefinitionsand obtain the effective beta function for a single coupling constant to the fifth order. The fixed point and the string susceptibility exponent are shown to approach the values obtained in the exact solution as the order of approximations becomes higher.