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Four-vertex model and random tilings

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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.

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Institute of Mathematics, St. Petersburg, Russia

    N. M. Bogoliubov

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  1. N. M. Bogoliubov
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Correspondence to N. M. Bogoliubov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 25–38, April, 2008.

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Bogoliubov, N.M. Four-vertex model and random tilings. Theor Math Phys 155, 523–535 (2008). https://doi.org/10.1007/s11232-008-0043-6

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  • DOI: https://doi.org/10.1007/s11232-008-0043-6

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