Domain wall partition function of the eight-vertex model with a non-diagonal reflecting end

TL;DR

This paper derives a determinant expression for the partition function of the eight-vertex model with a non-diagonal reflecting boundary, revealing a simplified single determinant form unlike the case without reflection.

Contribution

It provides the first explicit determinant formula for the eight-vertex model with a non-diagonal reflecting end using the Drinfeld twist method.

Findings

Partition function expressed as a single determinant.

Explicit determinant formula derived for non-diagonal reflecting boundary.

Contrasts with the case without reflection boundary.

Abstract

With the help of the Drinfeld twist or factorizing F-matrix for the eight-vertex SOS model, we obtain the explicit determinant expression of the partition function of the eight-vertex model with a generic non-diagonal reflecting end and domain wall boundary condition. Our result shows that, contrary to the eight-vertex model without a reflection end, the partition function can be expressed as a single determinant.