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Three-coloring statistical model with domain wall boundary conditions: Functional equations

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Abstract

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.

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References

  1. R. J. Baxter, J. Math. Phys., 11, 3116–3124 (1970).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  2. R. J. Baxter, Exactly Solved Models in Statistical Mechanics, Acad. Press, London (1982).

    MATH  Google Scholar 

  3. Yu. G. Stroganov, “General properties and special solutions of the triangle equation: Calculation of the partition functions for several models on a planar lattice [in Russian],” Candidate’s dissertation, Inst. High Energy Physics, Protvino (1982).

    Google Scholar 

  4. Yu. G. Stroganov, Phys. Lett. A, 74, 116–118 (1979).

    Article  MathSciNet  ADS  Google Scholar 

  5. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (4th ed.), Cambridge Univ. Press, Cambridge (1996).

    MATH  Google Scholar 

  6. A. Lenard, J. Math. Phys., 2, 682–693 (1961).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Yu. G. Stroganov, Theor. Math. Phys., 146, 53–62 (2006); arXiv:math-ph/0204042v3 (2002).

    Article  MathSciNet  Google Scholar 

  8. A. V. Razumov and Yu. G. Stroganov, Theor. Math. Phys., 141, 1609–1630 (2004); arXiv:math-ph/0312071v1 (2003).

    Article  MathSciNet  Google Scholar 

  9. A. G. Izergin, Sov. Phys. Dokl., 32, 878–879 (1987).

    ADS  Google Scholar 

  10. V. E. Korepin, Comm. Math. Phys., 86, 391–418 (1982).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. P. A. Pearce and K. A. Seaton, Phys. Rev. Lett., 60, 1347–1350 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  12. R. J. Baxter, Ann. Phys., 76, 25–47 (1973).

    Article  MathSciNet  ADS  Google Scholar 

  13. H. Rosengren, Adv. Appl. Math., 43, 137–155 (2009); arXiv:0801.1229v2 [math.CO] (2008).

    Article  MATH  MathSciNet  Google Scholar 

  14. N. M. Bogoliubov, A. G. Izergin, and V. E. Korepin, Correlation Functions of Integrable Systems and Quantum Method of the Inverse Problem [in Russian], Nauka, Moscow (1992).

    Google Scholar 

  15. G. Kuperberg, Internat. Math. Res. Notices, 1996, 139–150 (1996); arXiv:math/9712207v1 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  16. W. H. Mills, D. P. Robbins, and H. Rumsey Jr., J. Combin. Theory A, 34, 340–359 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  17. W. H. Mills, D. P. Robbins, and H. Rumsey Jr., Invent. Math., 66, 73–87 (1982).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. D. Zeilberger, New York J. Math., 2, 59–68 (1996); arXiv:math/9606224v1 (1996).

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute for High Energy Physics, Protvino, Moscow Oblast, Russia

    A. V. Razumov & Yu. G. Stroganov

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  1. A. V. Razumov
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  2. Yu. G. Stroganov
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Correspondence to A. V. Razumov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 161, No. 1, pp. 3–20, October, 2009.

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Razumov, A.V., Stroganov, Y.G. Three-coloring statistical model with domain wall boundary conditions: Functional equations. Theor Math Phys 161, 1325–1339 (2009). https://doi.org/10.1007/s11232-009-0119-y

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