Partition function of the eight-vertex model with domain wall boundary condition

TL;DR

This paper derives recursive relations and explicit formulas for the partition function of the eight-vertex model with domain wall boundary conditions, connecting to known results in the six-vertex model in certain limits.

Contribution

It provides the first explicit expression for the domain wall partition function of the eight-vertex model, extending known results from the six-vertex case.

Findings

Explicit recursive relations for the partition function

Closed-form expression for the partition function

Results reduce to six-vertex model in specific limits

Abstract

We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model.