Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2021
• Hauptverfasser: Minin, Mikhail D., Pronko, Andrei G.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2021
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/211416
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties. Mikhail D. Minin and Andrei G. Pronko. SIGMA 17 (2021), 111, 29 pages

We consider the six-vertex model with the rational weights on an × square lattice, ≤ , with partial domain wall boundary conditions. We study the one-point function at the boundary where the free boundary conditions are imposed. For a finite lattice, it can be computed by the quantum inverse scattering method in terms of determinants. In the large limit, the result boils down to an explicit terminating series in the parameter of the weights. Using the saddle-point method for an equivalent integral representation, we show that as next tends to infinity, the one-point function demonstrates a step-wise behavior; in the vicinity of the step, it scales as the error function. We also show that the asymptotic expansion of the one-point function can be computed from a second-order ordinary differential equation.