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Teoreticheskaya i Matematicheskaya Fizika, 2008, Volume 155, Number 1, Pages 25–38
DOI: https://doi.org/10.4213/tmf6190 (Mi tmf6190) 		 
This article is cited in 23 scientific papers (total in 23 papers)

Four-vertex model and random tilings

N. M. Bogolyubov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (470 kB) Citations (23)
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DOI: https://doi.org/10.4213/tmf6190
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.
English version:
Theoretical and Mathematical Physics, 2008, Volume 155, Issue 1, Pages 523–535
DOI: https://doi.org/10.1007/s11232-008-0043-6
Bibliographic databases:
Language: Russian
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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  • https://www.mathnet.ru/eng/tmf/v155/i1/p25
    • This publication is cited in the following 23 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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