On the $D_n$ Spin Vertex Models for Odd $n$

TL;DR

This paper investigates the $D_n$ spin vertex models for odd $n$, focusing on the $n=3$ and $n=5$ cases, describing their Boltzmann weights using crossing symmetry and the anti-spinor representation.

Contribution

It introduces explicit Boltzmann weights for $D_n$ spin vertex models with odd $n$, utilizing crossing symmetry and anti-spinor representations, specifically for $n=3$ and $n=5$.

Findings

Explicit Boltzmann weights for $n=3$ and $n=5$ models

Use of crossing symmetry to derive weights from known representations

Extension of $D_n$ models to include anti-spinor representations

Abstract

Solvable vertex models in two dimensions are of importance in conformal field theory, phase transitions and integrable models. We consider here the $D_n$ spin vertex models, for $n$ which is odd. The models involve also the anti--spinor representation. We describe here the Boltzmann weights for these representations using crossing symmetry from the previously known spinor representations. For calculation reasons we limit ourself to the $n=3$ and $n=5$ cases, which are described explicitly.