Exact results for the six-vertex model with domain wall boundary conditions and a partially reflecting end

Abstract

The trigonometric six-vertex model with domain wall boundary conditions and one partially reflecting end on a lattice of size 2ntimes m, mle n, is considered. The partition function is computed using the Izergin–Korepin method, generalizing the result of Foda and Zarembo from the rational to the trigonometric case. Thereafter, we specify the parameters in Kuperberg’s way to get a formula for the number of states as a determinant of Wilson polynomials. We relate this to a new type of alternating sign matrices, similar to how the six-vertex model with domain wall boundary conditions is related to normal alternating sign matrices. In an appendix, we compute the partition function again, showing that it is also possible to find it with the method of Foda and Wheeler.