Exact results for the six-vertex model with domain wall boundary conditions and a partially reflecting end
Journal article, 2022

The trigonometric six-vertex model with domain wall boundary conditions and one partially reflecting end on a lattice of size 2 n× m, m≤ 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.

Partition function

Reflecting end

Domain wall boundary conditions

Triangular K-matrix

Six-vertex model

Author

Linnea Hietala

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Uppsala University

Letters in Mathematical Physics

0377-9017 (ISSN) 1573-0530 (eISSN)

Vol. 112 2 41

Subject Categories

Computational Mathematics

Fluid Mechanics and Acoustics

Mathematical Analysis

DOI

10.1007/s11005-022-01530-5

More information

Latest update

5/3/2022 1