Functional relations in nineteen-vertex models with domain-wall boundaries

TL;DR

This paper investigates the functional properties of partition functions in nineteen-vertex models with domain-wall boundaries, deriving functional equations from the Yang-Baxter algebra for specific models.

Contribution

It introduces a unified approach to describe partition functions of nineteen-vertex models with boundary conditions using functional equations.

Findings

Partition functions obey functional equations from Yang-Baxter algebra

Unified description for Izergin-Korepin and Fateev-Zamolodchikov models

Functional relations characterize boundary effects in vertex models

Abstract

This work is concerned with functional properties shared by partition functions of nineteen-vertex models with domain-wall boundary conditions. In particular, we describe both Izergin-Korepin and Fateev-Zamolodchikov models with the aforementioned boundary conditions and show their partition functions are governed by a system of functional equations originated from the associated Yang-Baxter algebra.