Geodesic
Three-coloring statistical model with domain wall boundary conditions: Functional equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 1, pp. 3-20 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the Baxter three-coloring model with boundary conditions of the domain wall type. In this case, it can be proved that the partition function satisfies some functional equations similar to the functional equations satisfied by the partition function of the six-vertex model for a special value of the crossing parameter.
Keywords: three-coloring model, partition function, functional equation. 
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A. V. Razumov; Yu. G. Stroganov. Three-coloring statistical model with domain wall boundary conditions: Functional equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 161 (2009) no. 1, pp. 3-20. http://geodesic.mathdoc.fr/item/TMF_2009_161_1_a0/

[1] R. J. Baxter, J. Math. Phys., 11:10 (1970), 3116–3124 | DOI | Zbl

[2] R. Bekster, Tochno reshaemye modeli v statisticheskoi mekhanike, Mir, M., 1985 | MR | MR | Zbl

[3] Yu. G. Stroganov, Obschie svoistva i chastnye resheniya uravneniya treugolnika. Vychislenie statisticheskoi summy dlya nekotorykh modelei na ploskoi reshetke, Dis. $\dots$ kand. fiz.-matem. nauk, IFBE, Protvino, 1982

[4] Yu. G. Stroganov, Phys. Lett. A, 74:1–2 (1979), 116–118 | DOI | MR

[5] E. T. Uitteker, G. N. Vatson, Kurs sovremennogo analiza, Gostekhizdat, L.-M., 1933–1934 | MR | Zbl

[6] A. Lenard, J. Math. Phys., 2:5 (1961), 682–693 | DOI | MR | Zbl

[7] Yu. G. Stroganov, TMF, 146:1 (2006), 65–76 ; arXiv: math-ph/0204042 | DOI | MR | Zbl

[8] A. V. Razumov, Yu. G. Stroganov, TMF, 141:3 (2004), 323–347 ; arXiv: math-ph/0312071 | DOI | MR | Zbl

[9] A. G. Izergin, Dokl. AN SSSR, 297:2 (1987), 331–333 | MR | Zbl

[10] V. E. Korepin, Comm. Math. Phys., 86:3 (1982), 391–418 | DOI | MR | Zbl

[11] P. A. Pearce, K. A. Seaton, Phys. Rev. Lett., 60:14 (1988), 1347–1350 | DOI | MR

[12] R. J. Baxter, Ann. Phys., 76:1 (1973), 25–47 | DOI | Zbl

[13] H. Rosengren, Adv. Appl. Math., 43:2 (2009), 137–155 ; arXiv: 0801.1229 | DOI | MR | Zbl

[14] N. M. Bogolyubov, A. G. Izergin, V. E. Korepin, Korrelyatsionnye funktsii integriruemykh sistem i kvantovyi metod obratnoi zadachi, Nauka, M., 1992 | MR | MR | Zbl

[15] G. Kuperberg, Int. Math. Res. Not., 1996:3 (1996), 139–150 ; arXiv: math/9712207 | DOI | MR | Zbl

[16] W. H. Mills, D. P. Robbins, H. Rumsey Jr., J. Combin. Theory A, 34:3 (1983), 340–359 | DOI | MR | Zbl

[17] W. H. Mills, D. P. Robbins, H. Rumsey Jr., Invent. Math., 66:1 (1982), 73–87 | DOI | MR | Zbl

[18] D. Zeilberger, New York J. Math., 2 (1996), 59–68 ; arXiv: math/9606224 | MR | Zbl