The nineteen-vertex model and alternating sign matrices. (19th January 2015)

• Record Type: Journal Article
• Authors: Hagendorf, Christian
• Is Part Of: Journal of statistical mechanics. (2015:Jan.)
• Publication Date: 2015-01-19
• Subjects: 1; 1/070 -- 1/100 -- 1/120; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/01/P01017
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: It is shown that the transfer matrix of the inhomogeneous nineteen-vertex model with certain diagonal twisted boundary conditions possesses a simple eigenvalue. This is achieved through the identification of a simple and completely explicit solution of its Bethe equations. The corresponding eigenvector is computed by means of the algebraic Bethe ansatz and both a simple component and its square norm are expressed in terms of the Izergin–Korepin determinant. In the homogeneous limit, the vector coincides with a supersymmetry singlet of the twisted spin-one XXZ chain. It is shown that in a natural polynomial normalisation scheme its square norm and the simple component coincide with generating functions for weighted enumeration of alternating sign matrices.