Nonlinear Renormalization Group Equation for Matrix Models

TL;DR

This paper derives a nonlinear exact renormalization group equation for matrix models, providing a new algorithm to determine critical points and exponents, with explicit results for one-matrix models.

Contribution

It introduces a nonlinear RG equation specific to matrix models and offers an algorithm to compute critical parameters exactly.

Findings

Derived a nonlinear RG equation for matrix models

Developed an algorithm for critical coupling and exponent determination

Calculated exact critical values for one-matrix models

Abstract

An exact renormalization group equation is derived for the free energy of matrix models. The renormalization group equation turns out to be nonlinear for matrix models, as opposed to linear for vector models. An algorithm for determining the critical coupling constant and the critical exponent is obtained. As concrete examples, one-matrix models with one and two coupling constants are analyzed and the exact values of the critical coupling constant and the associated critical exponent are found.