On the partition function of the $Sp(2n)$ integrable vertex model

TL;DR

This paper analyzes the partition function of the integrable $Sp(2n)$ vertex model, deriving functional relations and computing the partition function per site for various representations in the thermodynamic limit.

Contribution

It introduces transfer matrix fusion relations for the $Sp(2n)$ vertex model and computes the partition function per site for fundamental and mixed representations.

Findings

Derived transfer matrix fusion relations for $Sp(2n)$ model

Computed partition function per site in the thermodynamic limit

Extended results to models mixing different representations

Abstract

We study the partition function per site of the integrable $Sp(2n)$ vertex model on the square lattice. We establish a set of transfer matrix fusion relations for this model. The solution of these functional relations in the thermodynamic limit allows us to compute the partition function per site of the fundamental $Sp(2n)$ representation of the vertex model. In addition, we also obtain the partition function of vertex models mixing the fundamental with other representations.