Large N expansion of the 2-matrix model

TL;DR

This paper introduces a recursive loop equation method to compute the large N topological expansion of the free energy in the 2-hermitian matrix model, demonstrated by calculating the first subleading term related to a statistical physics model on a discretized torus.

Contribution

The paper develops a recursive approach based on loop equations to systematically compute the large N expansion terms for the 2-matrix model, including the first subleading correction.

Findings

Successfully computed the first subleading free energy term.

Demonstrated the method on a statistical physics model on a discretized torus.

Provided a systematic recursive framework for large N expansions.

Abstract

We present a method, based on loop equations, to compute recursively all the terms in the large $N$ topological expansion of the free energy for the 2-hermitian matrix model. We illustrate the method by computing the first subleading term, i.e. the free energy of a statistical physics model on a discretized torus.