Geodesic
The partition function of the four-vertex model in a special external field
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 25, Tome 473 (2018), pp. 77-84

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The exactly solvable four-vertex model on a square grid with the fixed boundary conditions in a presence of a special external field is considered. Namely, we study a system in a linear field acting on the central column of a grid. The partition function of the model is calculated by Quantum Inverse Scattering Method. The answer is written in the determinantal form. 
@article{ZNSL_2018_473_a4,
     author = {N. Bogoliubov and C. Malyshev},
     title = {The partition function of the four-vertex model in a special external field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {77--84},
     publisher = {mathdoc},
     volume = {473},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_473_a4/}
}
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N. Bogoliubov; C. Malyshev. The partition function of the four-vertex model in a special external field. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 25, Tome 473 (2018), pp. 77-84. http://geodesic.mathdoc.fr/item/ZNSL_2018_473_a4/