Renormalization Group for Matrix Models with Branching Interactions

TL;DR

This paper introduces a renormalization group method for matrix models with branching interactions, accurately determining critical points and exponents, and extends to two-matrix models including the Ising model.

Contribution

The authors develop a novel RG approach for matrix models with branching interactions and successfully generalize it to two-matrix models, capturing critical behavior.

Findings

Accurate determination of critical points and exponents for one-matrix models.

Extension of the method to two-matrix models including the Ising critical points.

Validation of the approach through precise results matching known critical phenomena.

Abstract

We develop a method to obtain the large N renormalization group flows for matrix models of 2 dimensional gravity plus branched polymers. This method gives precise results for the critical points and exponents for one matrix models. We show that it can be generalized to two matrices models and we recover the Ising critical points.