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

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 that their partition functions are governed by a system of functional equations originating from the associated Yang-Baxter algebra. Published under license by AIP Publishing