Q-states Potts model on a random planar lattice

TL;DR

This paper derives the critical and tricritical scaling exponents of the q-states Potts model on a random planar lattice using matrix models, providing explicit results especially for q=3.

Contribution

It introduces a matrix-model approach to compute scaling exponents of the Potts model coupled to gravity, extending methods from the $O(n)$ model.

Findings

Derived algebraic equations for scaling exponents

Explicit scaling law for q=3 case

Method applicable to other q-values

Abstract

We propose a matrix-model derivation of the scaling exponents of the critical and tricritical q-states Potts model coupled to gravity on a sphere. In close analogy with the $O(n)$ model, we reduce the determination of the one-loop-to-vacuum expectation to the resolution of algebraic equations; and find the explicit scaling law for the case q=3.