Geodesic
Evidence for a Phase Transition in Three-Dimensional Lattice Models
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 369-382 Cet article a éte moissonné depuis la source Math-Net.Ru

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It was recently discovered that an eigenvector structure of commutative families of layer-to-layer matrices in three-dimensional lattice models is described by a two-dimensional spin lattice generalizing the notion of one-dimensional spin chains. We conjecture the relations between the two-dimensional spin lattice in the thermodynamic limit and the phase structure of three-dimensional lattice models. We consider two simplest cases: the homogeneous spin lattice related to the Zamolodchikov–Bazhanov–Baxter model and a “chess spin lattice” related to the Stroganov–Mangazeev elliptic solution of the modified tetrahedron equation. Evidence for the phase transition is obtained in the second case.
Keywords: three,dimensional integrable models, Zamolodchikov–Bazhanov–Baxter model. 
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     title = {Evidence for {a~Phase} {Transition} in {Three-Dimensional} {Lattice} {Models}},
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S. M. Sergeev. Evidence for a Phase Transition in Three-Dimensional Lattice Models. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 369-382. http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a1/

[1] A. B. Zamolodchikov, ZhETF, 79 (1980), 641–664 ; A. B. Zamolodchikov, Commun. Math. Phys., 79 (1981), 489–505 | MR | DOI | MR

[2] R. J. Baxter, Commun. Math. Phys., 88 (1983), 185–205 ; Phys. Rev. Lett., 53 (1984), 1795–1798 ; Physica D, 18 (1986), 321–347 | DOI | MR | DOI | MR | DOI | MR | Zbl

[3] V. V. Bazhanov, R. J. Baxter, J. Stat. Phys., 69 (1992), 453–485 | DOI | MR | Zbl

[4] S. M. Sergeev, V. V. Mangazeev, Yu. G. Stroganov, J. Stat. Phys., 82 (1996), 31–50 | DOI | MR

[5] R. J. Baxter, P. J. Forrester, J. Phys. A, 18 (1985), 1483–1497 | DOI | MR

[6] V. V. Mangazeev, Yu. G. Stroganov, Mod. Phys. Lett. A, 8 (1993), 3475–3482 ; V. V. Mangazeev, S. M. Sergeev, Yu. G. Stroganov, Int. J. Mod. Phys. A, 9 (1994), 5517–5530 ; H. E. Boos, V. V. Mangazeev, S. M. Sergeev, Yu. G. Stroganov, Int. J. Mod. Phys. A, 10 (1995), 4041–4064 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR

[7] S. Sergeev, J. Phys. A, 32 (1999), 5693–5714 ; С. М. Сергеев, ТМФ, 124:3 (2000), 391–409 ; Зап. научн. семин. ПОМИ, 269, 2000, 292–307 | DOI | MR | Zbl | DOI | MR | Zbl | Zbl

[8] S. Z. Pakulyak, S. M. Sergeev, TMF, 136:1 (2003), 30–51 ; E-print nlin.SI/0209019 | DOI | MR

[9] G. von Gehlen, S. Pakuliak, S. Sergeev, J. Phys. A, 36 (2003), 975–998 ; E-print nlin.SI/0208035 | DOI | MR | Zbl

[10] S. M. Sergeev, TMF, 138:2 (2004), 269–282 | DOI | MR | Zbl

[11] Ch. Fan, F. Y. Wu, Phys. Rev. B, 2 (1970), 723–733 | DOI

[12] E. T. Uitteker, Dzh. N. Vatson, Kurs sovremennogo analiza, Fizmatgiz, M., 1962