Geodesic
Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 125-144

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The five-vertex model on a square lattice with fixed boundary conditions, which corresponds to the weighted (with the weight $q$ per elementary cube) enumerations of boxed plane partition is considered. The one-point correlation function of the model describing the probability of a given state on an edge (polarization) is calculated. This generalises the similar result obtained previously by the authors for the unweighed (weighted with the weight $q=1$) enumerations of plane partitions. 
@article{ZNSL_2012_398_a6,
     author = {V. S. Kapitonov and A. G. Pronko},
     title = {Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {125--144},
     publisher = {mathdoc},
     volume = {398},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a6/}
}
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V. S. Kapitonov; A. G. Pronko. Weighted enumerations of boxed plane partitions and inhomogeneous five-vertex model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 22, Tome 398 (2012), pp. 125-144. http://geodesic.mathdoc.fr/item/ZNSL_2012_398_a6/