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TMF, 2008, Volume 155, Number 1, Pages 25–38 (Mi tmf6190)  

This article is cited in 9 scientific papers (total in 9 papers)

Four-vertex model and random tilings

N. M. Bogolyubov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: We consider the exactly solvable four-vertex model on a square lattice with different boundary conditions. Using the algebraic Bethe ansatz method allows calculating the partition function of the model. For fixed boundary conditions, we establish the connection between the scalar product of the state vectors and the generating function of the column- and row-strict boxed plane partitions. We discuss the tiling model on a periodic lattice.

Keywords: integrable model, Bethe ansatz, plane partition

DOI: https://doi.org/10.4213/tmf6190

Full text: PDF file (470 kB)
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English version:
Theoretical and Mathematical Physics, 2008, 155:1, 523–535

Bibliographic databases:


Citation: N. M. Bogolyubov, “Four-vertex model and random tilings”, TMF, 155:1 (2008), 25–38; Theoret. and Math. Phys., 155:1 (2008), 523–535

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tmf/v155/i1/p25

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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. V. S. Kapitonov, A. G. Pronko, “The five-vertex model and boxed plane partitions”, J. Math. Sci. (N. Y.), 158:6 (2009), 858–867  mathnet  crossref  zmath
    2. Nikolay M. Bogolyubov, “Determinantal Representation of the Time-Dependent Stationary Correlation Function for the Totally Asymmetric Simple Exclusion Model”, SIGMA, 5 (2009), 052, 11 pp.  mathnet  crossref  mathscinet  zmath
    3. N. M. Bogolyubov, “Five vertex model with fixed boundary conditions”, St. Petersburg Math. J., 21:3 (2010), 407–421  mathnet  crossref  mathscinet  zmath  isi
    4. N. M. Bogolyubov, K. L. Malyshev, “Ising limit of a Heisenberg $XXZ$ magnet and some temperature correlation functions”, Theoret. and Math. Phys., 169:2 (2011), 1517–1529  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    5. V. S. Kapitonov, A. G. Pronko, “Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model”, J. Math. Sci. (N. Y.), 192:1 (2013), 70–80  mathnet  crossref  mathscinet
    6. Motegi K., Sakai K., “Vertex Models, Tasep and Grothendieck Polynomials”, J. Phys. A-Math. Theor., 46:35 (2013), 355201  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. A. G. Pronko, “The five-vertex model and enumerations of plane partitions”, J. Math. Sci. (N. Y.), 213:5 (2016), 756–768  mathnet  crossref  mathscinet
    8. N. M. Bogolyubov, K. L. Malyshev, “Integrable models and combinatorics”, Russian Math. Surveys, 70:5 (2015), 789–856  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. N. Bogoliubov, C. Malyshev, “The partition function of the four-vertex model in a special external field”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 25, K 70-letiyu M. A. Semenova-Tyan-Shanskogo, Zap. nauchn. sem. POMI, 473, POMI, SPb., 2018, 77–84  mathnet
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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