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TMF, 2009, Volume 161, Number 1, Pages 3–20 (Mi tmf6415)  

This article is cited in 10 scientific papers (total in 10 papers)

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

A. V. Razumov, Yu. G. Stroganov

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

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.

Keywords: three-coloring model, partition function, functional equation

DOI: https://doi.org/10.4213/tmf6415

Full text: PDF file (537 kB)
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English version:
Theoretical and Mathematical Physics, 2009, 161:1, 1325–1339

Bibliographic databases:

Received: 08.12.2008

Citation: A. V. Razumov, Yu. G. Stroganov, “Three-coloring statistical model with domain wall boundary conditions: Functional equations”, TMF, 161:1 (2009), 3–20; Theoret. and Math. Phys., 161:1 (2009), 1325–1339

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Razumov, Yu. G. Stroganov, “Three-coloring statistical model with domain wall boundary conditions: Trigonometric limit”, Theoret. and Math. Phys., 161:2 (2009), 1451–1459  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. J.-Ch. Aval, “The symmetry of the partition function of some square ice models”, Theoret. and Math. Phys., 161:3 (2009), 1582–1589  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Rosengren H., “The three-colour model with domain wall boundary conditions”, Adv in Appl Math, 46:1–4 (2011), 481–535  crossref  mathscinet  zmath  isi  scopus
    4. Galleas W., “Multiple integral representation for the trigonometric SOS model with domain wall boundaries”, Nuclear Phys B, 858:1 (2012), 117–141  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    5. Galleas W., “Refined Functional Relations for the Elliptic Sos Model”, Nucl. Phys. B, 867:3 (2013), 855–871  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Behrend R.E., “Multiply-Refined Enumeration of Alternating Sign Matrices”, Adv. Math., 245 (2013), 439–499  crossref  mathscinet  zmath  isi  elib  scopus
    7. Galleas W., “Functional Relations and the Yang–Baxter Algebra”, Xxist International Conference on Integrable Systems and Quantum Symmetries (Isqs21), Journal of Physics Conference Series, 474, eds. Burdik C., Navratil O., Posta S., IOP Publishing Ltd, 2013  crossref  mathscinet  isi  scopus
    8. Rosengren H., “Elliptic Pfaffians and solvable lattice models”, J. Stat. Mech.-Theory Exp., 2016, 083106  crossref  mathscinet  isi  elib  scopus
    9. Behrend R.E. Fischer I. Konvalinka M., “Diagonally and Antidiagonally Symmetric Alternating Sign Matrices of Odd Order”, Adv. Math., 315 (2017), 324–365  crossref  mathscinet  zmath  isi  scopus
    10. Galleas W., “On the Elliptic Gl(2) Solid-on-Solid Model: Functional Relations and Determinants”, J. Math. Phys., 60:2 (2019), 023503  crossref  mathscinet  zmath  isi  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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