Solution of Potts-3 and Potts-\infty Matrix Models with the Equations of Motion Method

TL;DR

This paper demonstrates how the equations of motion method can be effectively used to solve Potts-3 and Potts-infinity matrix models, providing algebraic solutions and insights into their scaling behavior.

Contribution

It introduces a new application of the equations of motion to solve complex Potts matrix models, simplifying their analysis.

Findings

Derived algebraic equations for the resolvents of the models

Analyzed the scaling behavior of the models

Showed the utility of equations of motion as a solving tool

Abstract

In this letter, we show how one can solve easily the Potts-3 + branching interactions and Potts-\infty matrix models, by the means of the equations of motion (loop equations). We give an algebraic equation for the resolvents of these models, and their scaling behaviour. This shows that the equations of motion can be a useful tool for solving such models.