Six-Vertex Model, Yang—Baxter Equations, and Orthogonal Polynomials Dr. Pavel Bleher, Indiana University-Purdue University Indianapolis Host: Igor Pritsker
Abstract: The six-vertex model is a two dimensional model of statistical mechanics. A special case of it is the square ice model. We will discuss an exact solution of the six-vertex model with domain wall boundary conditions. This exact solution is based on the Yang—Baxter equations. We will explain how to use the Yang—Baxter equations to derive the Izergin—Korepin determinantal formula for the partition function. Then we will explain the Zinn-Justin transform, which reduces the Izergin—Korepin determinant to orthogonal polynomials. Our main result is an asymptotic expansion of the partition function of the six-vertex model as the size of the system goes to infinity, and it is based on the Riemann—Hilbert approach to the asymptotic analysis of orthogonal polynomials, of both continuous and discrete type.
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