Geodesic
One-point function of the four-vertex model
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 39-53

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We consider the four-vertex model on a finite domain of the square lattice with the so-called scalar-product boundary conditions. It can be described in terms of non-intersecting lattice paths which are additionally restricted in their propagation in one of the two spacial directions. We compute the one-point function measuring the probability to obtain a path on a given lattice edge. We also relate this function with another one-point function which can be regarded as a local anti-ferroelectric order parameter. 
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     author = {N. M. Bogolyubov and A. G. Pronko},
     title = {One-point function of the four-vertex model},
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     publisher = {mathdoc},
     volume = {509},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a2/}
}
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N. M. Bogolyubov; A. G. Pronko. One-point function of the four-vertex model. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 28, Tome 509 (2021), pp. 39-53. http://geodesic.mathdoc.fr/item/ZNSL_2021_509_a2/