Introduction to Monte Carlo for Matrix Models

TL;DR

This paper demonstrates the effectiveness of Monte Carlo methods in analyzing large N matrix models, validating results against known solutions and providing new insights into complex multi-matrix models with accessible Python tools.

Contribution

It introduces Monte Carlo techniques for large N matrix models, validates them against existing methods, and offers new results for previously unsolved multi-matrix models with open-source Python programs.

Findings

Monte Carlo results agree with exact solutions for one and two-matrix models.

New results obtained for complex multi-matrix models.

Python programs provided for easy adaptation and study of various potentials.

Abstract

We consider a wide range of matrix models and study them using the Monte Carlo technique in the large $N$ limit. The results we obtain agree with exact analytic expressions and recent numerical bootstrap methods for models with one and two matrices. We then present new results for several unsolved multi-matrix models where no other tool is yet available. In order to encourage an exchange of ideas between different numerical approaches to matrix models, we provide programs in Python that can be easily modified to study potentials other than the ones discussed. These programs were tested on a laptop and took between a few minutes to several hours to finish depending on the model, $N$, and the required precision.