Remarks on the Star-Triangle Relation in the Baxter-Bazhanov Model

TL;DR

This paper demonstrates that the restricted star-triangle relation in the Baxter-Bazhanov model can be derived from the chiral Potts model's relation or the star-square relation, clarifying a previously guessed connection.

Contribution

It establishes a link between the restricted star-triangle relation and other known relations, providing a new perspective on the Baxter-Bazhanov model.

Findings

The restricted star-triangle relation can be derived from the chiral Potts model.

The star-square relation also leads to the restricted star-triangle relation.

The paper confirms a previously suggested guess about these relations.

Abstract

In this letter we show that the restricted star-triangle relation introduced by Bazhanov and Baxter can be obtained either from the star-triangle relation of chiral Potts model or from the star-square relation which is proposed by Kashaev $et ~al$ and give a response of the guess which is suggested by Bazhanov and Baxter in Ref. \cite{b2}.