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Algebra i Analiz, 2009, Volume 21, Issue 3, Pages 58–78 (Mi aa1139)  
This article is cited in 13 scientific papers (total in 13 papers)

Research Papers

Five vertex model with fixed boundary conditions

N. M. Bogolyubov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (306 kB) Citations (13)
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Abstract: The exactly solvable five-vertex model on a square lattice with fixed boundary conditions is considered. Application of the algebraic Bethe ansatz makes it possible to express the partition function and the boundary correlation functions of the nonhomogeneous model in the determinantal form. The relationship established between the homogeneous model and plane partitions helps to calculate its partition function.
Received: 01.04.2008
English version:
St. Petersburg Mathematical Journal, 2010, Volume 21, Issue 3, Pages 407–421
DOI: https://doi.org/10.1090/S1061-0022-10-01100-3
Bibliographic databases:
Document Type: Article
MSC: 81T25
Language: Russian
Citation: N. M. Bogolyubov, “Five vertex model with fixed boundary conditions”, Algebra i Analiz, 21:3 (2009), 58–78; St. Petersburg Math. J., 21:3 (2010), 407–421
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/aa1139
  • https://www.mathnet.ru/eng/aa/v21/i3/p58
    • This publication is cited in the following 13 articles:
    1. Ivan N. Burenev, Andrei G. Pronko, “Thermodynamics of the Five-Vertex Model with Scalar-Product Boundary Conditions”, Commun. Math. Phys., 405:6 (2024)  crossref
    2. N. M. Bogoliubov, C. L. Malyshev, “Scalar Product of the Five-Vertex Model and Complete Symmetric Polynomials”, J Math Sci, 2024  crossref
    3. N. M. Bogolyubov, C. L. Malyshev, “Scalar product of the five-vertex model and complete symmetric polynomials”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 29, Zap. nauchn. sem. POMI, 520, POMI, SPb., 2023, 124–138  mathnet
    4. I. N. Burenev, A. G. Pronko, “Quantum Hamiltonians Generated by the R-Matrix of the Five-Vertex Model”, J Math Sci, 264:3 (2022), 271  crossref
    5. Burenev I.N., Pronko A.G., “Determinant Formulas For the Five-Vertex Model”, J. Phys. A-Math. Theor., 54:5 (2021), 055008  crossref  mathscinet  isi
    6. de Gier J., Kenyon R., Watson S.S., “Limit Shapes For the Asymmetric Five Vertex Model”, Commun. Math. Phys., 385:2 (2021), 793–836  crossref  mathscinet  isi
    7. I. N. Burenev, A. G. Pronko, “Kvantovye gamiltoniany porozhdaemye RR-matritsei pyativershinnoi modeli”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 27, Zap. nauchn. sem. POMI, 494, POMI, SPb., 2020, 103–124  mathnet
    8. Bogoliubov N.M., “Four-Vertex Model in the Linearly Growing External Field Under the Fixed and Periodic Boundary Conditions”, Phys. Part. Nuclei, 51:4 (2020), 429–433  crossref  isi  scopus
    9. Bogoliubov N., Malyshev C., “The Partition Function of the Four-Vertex Model in Inhomogeneous External Field and Trace Statistics”, J. Phys. A-Math. Theor., 52:49 (2019), 495002  crossref  mathscinet  isi
    10. Yu.V. Bushkova, G.E. Ivanova, L.V. Stakhovskaya, A.A. Frolov, “Brain-computer-interface technology with multisensory feedback for controlled ideomotor training in the rehabilitation of stroke patients”, BRSMU, 2019, no. 2019;6, 27  crossref
    11. J. Math. Sci. (N. Y.), 242:5 (2019), 742–752  mathnet  crossref
    12. 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
    13. 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
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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