Hermitian Matrix Model with Plaquette Interaction

TL;DR

This paper introduces an exactly solvable hermitian matrix model with plaquette interaction, revealing its critical properties and universality class as an $O(n)$ model on a random lattice for certain parameter ranges.

Contribution

It reformulates a hermitian matrix model with plaquette interaction as an $O(n)$ model on a random lattice and solves it exactly, analyzing its critical behavior.

Findings

Model belongs to the same universality class as the $O(n)$ model for $n$ in (-2, 2]

Exact solution of the hermitian matrix model with plaquette interaction

Identification of critical properties and universality class

Abstract

We study a hermitian $(n+1)$-matrix model with plaquette interaction, $\sum_{i=1}^n MA_iMA_i$. By means of a conformal transformation we rewrite the model as an $O(n)$ model on a random lattice with a non polynomial potential. This allows us to solve the model exactly. We investigate the critical properties of the plaquette model and find that for $n\in]-2,2]$ the model belongs to the same universality class as the $O(n)$ model on a random lattice.