RUS  ENG
Full version
JOURNALS // Zapiski Nauchnykh Seminarov POMI

Zap. Nauchn. Sem. POMI, 2023, Volume 520, Pages 17–49 (Mi znsl7312)

Boltzmann weights and fusion procedure for the rational seven-vertex SOS model
P. V. Antonenko, P. A. Valinevich

References

1. R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985  mathscinet
2. E. Date, M. Jimbo, T. Miwa and M. Okado, “Fusion of the eight vertex SOS model”, Lett. Math. Phys., 12 (1986), 209–215  crossref  mathscinet
3. E. Date, M. Jimbo, A. Kuniba, T. Miwa and M. Okado, “Exactly solvable SOS models II”, Adv. Stud. Pure Math., 16 (1988), 17–122  crossref  mathscinet  zmath
4. P. A. Valinevich, P. V. Antonenko, “Universalnaya $R$-matritsa dlya ratsionalnoi semivershinnoi modeli”, Zap. nauchn. sem. POMI, 487, 2019, 100–105  mathnet
5. D. Chicherin, S. E. Derkachov, V. P. Spiridonov, “From principal series to finite-dimensional solutions of the Yang-Baxter equation”, SIGMA, 12 (2016), 028  mathnet  mathscinet  zmath
6. K. Atalikov, A. Zotov, Higher rank generalization of $11$-vertex rational $R$-matrix: IRF-Vertex relations and associative Yang–Baxter equation, arXiv: 2303.02391
7. S. Derkachov, D. Karakhanyan, R. Kirschner, “Universal $R$ operator with Jordanian deformation of conformal symmetry”, Nucl. Phys. B, 681 (2004), 295–323  crossref  mathscinet  zmath
8. P. A. Valinevich, S. E. Derkachev, A. P. Isaev, A. V. Komisarchuk, “Ortogonalnye polinomy, $6j$-simvoly i statisticheskie vesa SOS-modelei”, Zap. nauchn. semin. POMI, 465, 2017, 105–134  mathnet
9. N. M. Bogolyubov, A. G. Izergin, V. E. Korepin, Korrelyatsionnye funktsii integriruemykh sistem i kvantovyi metod obratnoi zadachi, Nauka, M., 1992  mathscinet
10. T. Kojima, H. Konno, R. Weston, “The vertex-face correspondence and correlation functions of the fusion eight-vertex model I: The general formalism”, Nucl. Phys. B, 720 (2005), 348–398  crossref  mathscinet  zmath
11. N. Slavnov, “Algebraicheskii anzats Bete”, Lekts. kursy NOTs, 27, 2017, 3–189  mathnet  mathnet  crossref  mathscinet
12. A. Antonov, K. Hasegawa, A. Zabrodin, “On trigonometric intertwining vectors and non-dynamical $R$-matrix for the Ruijsenaars model”, Nucl. Phys. B, 503 (1997), 747–770  crossref  mathscinet  zmath
13. H. J. de Vega, H. J. Giacomini, “Intertwining vectors and the connection between critical vertex and SOS models”, J. Phys. A: Math. Gen., 22 (1989), 2759–2779  crossref  mathscinet  zmath
14. E. K. Sklyanin, “Boundary conditions for integrable quantum systems”, J. Phys. A: Math. Gen., 21 (1988), 2375–2389  crossref  mathscinet  zmath
15. H. Saleur, J. B. Zuber, Integrable lattice models and quantum groups, Lectures at the 1990 Trieste Spring School, Saclay SPhT/90-071  mathscinet
16. P. P. Kulish, N. Yu. Reshetikhin and E. K. Skylyanin, “Yang–Baxter equation and representation theory: I”, Lett. Math. Phys., 5 (1981), 393–403  crossref  mathscinet  zmath
17. Kulish P.P., Sklyanin E.K., “Quantum spectral transform method. Recent developments”, Integrable Quantum Field Theories, Lecture Notes in Physics, 151, eds. Hietarinta J., Montonen C., Springer, Berlin–Heidelberg, 1982  mathscinet
18. P. P. Kulish, A. A. Stolin, “Deformed Yangians and integrable models”, Czech. J. Phys., 47 (1997), 1207–1212, arXiv: q-alg/9708024  crossref  mathscinet  zmath
19. R. Baxter, “Eight-vertex model in lattice statistics and one-dimensional anisotropic Heisenberg chain: II. Equivalence to a generalized ice-type lattice model”, Ann. Physics, 76 (1973), 25–47  crossref  zmath
20. V. Pasquier, “Etiology of IRF models”, Commun. Math. Phys., 118 (1988), 355–364  crossref  mathscinet  zmath


© Steklov Math. Inst. of RAS, 2025