A new representation for the partition function of the six vertex model with domain wall boundaries

TL;DR

This paper introduces a novel sum-over-permutations representation for the six vertex model's partition function with domain wall boundaries, simplifying the partial homogeneous limit and revealing its satisfaction of a linear PDE.

Contribution

The paper presents a new permutation-based representation of the partition function, enabling easier analysis and computation for the six vertex model with domain wall boundaries.

Findings

Partition function expressed as a sum over permutations

Partial homogeneous limit can be taken trivially

Partition function satisfies a linear PDE

Abstract

We obtain a new representation for the partition function of the six vertex model with domain wall boundaries using a functional equation recently derived by the author. This new representation is given in terms of a sum over the permutation group where the partial homogeneous limit can be taken trivially. We also show by construction that this partition function satisfies a linear partial differential equation.