Star--Matrix Models

TL;DR

This paper introduces a modified Q-matrix method to analyze complex star-matrix models, providing explicit formulas for critical behavior in specific cases and confirming results with existing approaches.

Contribution

The paper develops a modified Q-matrix approach tailored for star-matrix models, enabling the derivation of explicit critical behavior formulas for special cases.

Findings

Results consistent with other methods.

Explicit formulas for q=2 and q=3 models.

Critical behavior matches Ising model on φ^3 lattice.

Abstract

The star-matrix models are difficult to solve due to the multiple powers of the Vandermonde determinants in the partition function. We apply to these models a modified Q-matrix approach and we get results consistent with those obtained by other methods.As examples we study the inhomogenous gaussian model on Bethe tree and matrix $q$-Potts-like model. For the last model in the special cases $q=2$ and $q=3$, we write down explicit formulas which determinate the critical behaviour of the system.For $q=2$ we argue that the critical behaviour is indeed that of the Ising model on the $\phi^3$ lattice.