Geodesic
Four-vertex model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 20, Tome 347 (2007), pp. 34-55

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Exactly solvable four-vertex model is considered on a square grid with the different boundary conditions. The application of the Algebraic Bethe Ansatz method allows to calculate the partition function of the model and to establish the connection of the scalar product of the state vectors with the generating function of the column and raw strict boxed plane partitions. The tiling model on a periodic grid is discussed. 
@article{ZNSL_2007_347_a2,
     author = {N. M. Bogolyubov},
     title = {Four-vertex model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {34--55},
     publisher = {mathdoc},
     volume = {347},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_347_a2/}
}
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N. M. Bogolyubov. Four-vertex model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 20, Tome 347 (2007), pp. 34-55. http://geodesic.mathdoc.fr/item/ZNSL_2007_347_a2/