Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties
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 scat...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2021 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2021
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211416 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862619151584985088 |
|---|---|
| author | Minin, Mikhail D. Pronko, Andrei G. |
| author_facet | Minin, Mikhail D. Pronko, Andrei G. |
| citation_txt | 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 |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-14T11:36:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211416 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T11:36:52Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Minin, Mikhail D. Pronko, Andrei G. 2026-01-02T08:28:15Z 2021 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 1815-0659 2020 Mathematics Subject Classification: 05A19; 05E05; 82B23 arXiv:2108.06190 https://nasplib.isofts.kiev.ua/handle/123456789/211416 https://doi.org/10.3842/SIGMA.2021.111 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. The authors thank N.M. Bogoliubov, F. Colomo, N. Reshetikhin, E. Sobko for stimulating discussions, and the anonymous referees for valuable remarks. This work was supported in part by the Russian Science Foundation, grant # 18-11-00297. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties Article published earlier |
| spellingShingle | Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties Minin, Mikhail D. Pronko, Andrei G. |
| title | Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties |
| title_full | Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties |
| title_fullStr | Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties |
| title_full_unstemmed | Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties |
| title_short | Boundary One-Point Function of the Rational Six-Vertex Model with Partial Domain Wall Boundary Conditions: Explicit Formulas and Scaling Properties |
| title_sort | boundary one-point function of the rational six-vertex model with partial domain wall boundary conditions: explicit formulas and scaling properties |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211416 |
| work_keys_str_mv | AT mininmikhaild boundaryonepointfunctionoftherationalsixvertexmodelwithpartialdomainwallboundaryconditionsexplicitformulasandscalingproperties AT pronkoandreig boundaryonepointfunctionoftherationalsixvertexmodelwithpartialdomainwallboundaryconditionsexplicitformulasandscalingproperties |