|
|
|
|
References
|
|
| |
| 1. |
W. Li, H. Park, M. Widom, “Finite-size scaling amplitudes in a random tiling model”, J. Phys. A: Math. Gen., 23 (1990), L573–L580 |
| 2. |
W. Li, H. Park, “Logarithmic singularity in the surface free energy near commensurate-incommensurate transitions”, J. Phys. A: Math. Gen., 24 (1991), 257–264 |
| 3. |
N. M. Bogoliubov, “Four-vertex model and random tilings”, Theor. Math. Phys., 155 (2008), 523–535 |
| 4. |
N. M. Bogoliubov, “Four-vertex model”, J. Math. Sci. (N.Y.), 151 (2008), 2816–2828 |
| 5. |
N. M. Bogolyubov, C. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70 (2015), 789–856 |
| 6. |
H. Cohn, M. Larsen, J. Propp, “The shape of a typical boxed plane partition”, New York J. Math., 4 (1998), 137–165 |
| 7. |
J. de Gier, R. Kenyon, S. S. Watson, “Limit shapes for the asymmetric five vertex model”, Commun. Math. Phys., 385 (2021), 793–836 |
| 8. |
A. G. Pronko, “The five-vertex model and enumerations of plane partitions”, J. Math. Sci. (N. Y.), 213 (2016), 756–768 |
| 9. |
P. Bleher, K. Liechty, “Six-vertex model with partial domain wall boundary conditions: Ferroelectric phase”, J. Math. Phys., 56 (2015), 023302 |
| 10. |
I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edn, Oxford University Press, Oxford, 1995 |
| 11. |
V. E. Korepin, N. M. Bogoliubov, A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions, Cambridge University Press, Cambridge, 1993 |
| 12. |
F. Colomo, G. Di Giulio, A. G. Pronko, “Six-vertex model on a finite lattice: integral representations for nonlocal correlation functions”, Nucl. Phys. B, 972 (2021), 115535 |
| 13. |
D. M. Bressoud, Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture, Cambridge University Press, Cambridge, 1999 |
| 14. |
M. L. Mehta, Random Matrices, 3rd. ed, Elsevier, Amsterdam, 2004 |
| 15. |
V. E. Korepin, P. Zinn-Justin, “Thermodynamic limit of the six-vertex model with domain wall boundary conditions”, J. Phys. A, 33 (2000), 7053–7066 |
| 16. |
O. F. Syljuasen, M. B. Zvonarev, “Monte-Carlo simulations of vertex models”, Phys. Rev. E, 70 (2004), 016118 |
| 17. |
D. Allison, N. Reshetikhin, “Numerical study of the $6$-vertex model with domain wall boundary conditions”, Ann. Inst. Fourier (Grenoble), 55 (2005), 1847–1869 |
| 18. |
V. S. Kapitonov, A. G. Pronko, “Six-vertex model as a Grassmann integral, one-point function, and the arctic ellipse”, Zap. Nauchn. Semin. POMI, 494, 2020, 168–218 |
| 19. |
P. Belov, N. Reshetikhin, The two-point correlation function in the six-vertex model, 2012, arXiv: 2012.05182 |