A method of calculation for the determinant of the Potts model transfer matrix

TL;DR

This paper presents a method to calculate the determinant of the transfer matrix for the 2D q-state Potts model by decomposing it, confirming a previously conjectured formula.

Contribution

The paper introduces a novel decomposition approach to compute the transfer matrix determinant, providing a proof for Chang and Shrock's conjecture.

Findings

Determinant of the Potts model transfer matrix is explicitly calculated.

The method confirms the conjectured formula by Chang and Shrock.

Decomposition of the transfer matrix simplifies the determinant calculation.

Abstract

By using a decomposition of the transfer matrix of the two dimensional $q$-state Potts Model to $V^{\prime}_1$ and $V_2$ its determinant is calculated. Our result is a proof for a conjectured formula by Chang and Shrock in [14].