Relation between Yang-Baxter and Pair Propagation Equations in 16-Vertex Models

TL;DR

This paper investigates the connection between Yang-Baxter and pair propagation equations in 16-vertex models, revealing discrepancies and identifying solvable models that do not satisfy Yang-Baxter equations.

Contribution

It demonstrates that in 16-vertex models, the equivalence between the two integrability conditions breaks down, providing explicit examples of solvable models lacking Yang-Baxter solutions.

Findings

Discrepancies between Yang-Baxter and pair propagation equations in 16-vertex models

Existence of exactly solvable 16-vertex models not satisfying Yang-Baxter equations

Contrast with 8-vertex models where the conditions are equivalent

Abstract

We study a relation between two integrability conditions, namely the Yang-Baxter and the pair propagation equations, in 2D lattice models. While the two are equivalent in the 8-vertex models, discrepancies appear in the 16-vertex models. As explicit examples, we find the exactly solvable 16-vertex models which do not satisfy the Yang-Baxter equations.