Abstract
An exactly solvable four-vertex model on a square grid with different boundary conditions is considered. The application of the Algebraic Bethe Ansatz method allows us to calculate the partition function of the model. For fixed boundary conditions, we establish a relation between the scalar product of state vectors with the generating function of column-and row-strict boxed plane partitions. A tiling model on a periodic grid is discussed. Bibliography: 33 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 347, 2007, pp. 34–55.
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Bogoliubov, N.M. Four-vertex model. J Math Sci 151, 2816–2828 (2008). https://doi.org/10.1007/s10958-008-9000-z
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DOI: https://doi.org/10.1007/s10958-008-9000-z