Geodesic
Some explicit results for the generalized emptiness formation probability of the six-vertex model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 24, Tome 465 (2017), pp. 157-173

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We study a multi-point correlation function of the six-vertex model on the square lattice with the domain wall boundary conditions which is called the generalized emptiness formation probability. This function describes probability of observing the ferroelectric order around all the vertices of any Ferrer diagram $\lambda$ at the top-left corner of the lattice. For the free-fermion model we derive and compare explicit formulas for this correlation function for two cases of diagram $\lambda$: the square and triangle. We found a connection of our formulas with the $\tau$-function of the sixth Painlevé equation. 
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     author = {A. V. Kitaev and A. G. Pronko},
     title = {Some explicit results for the generalized emptiness formation probability of the six-vertex model},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {157--173},
     publisher = {mathdoc},
     volume = {465},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_465_a9/}
}
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A. V. Kitaev; A. G. Pronko. Some explicit results for the generalized emptiness formation probability of the six-vertex model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 24, Tome 465 (2017), pp. 157-173. http://geodesic.mathdoc.fr/item/ZNSL_2017_465_a9/