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 nonintersecting 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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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 509, 2021, pp. 39–53.
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Bogolyubov, N.M., Pronko, A.G. One-Point Function of the Four-Vertex Model. J Math Sci 275, 249–258 (2023). https://doi.org/10.1007/s10958-023-06677-7
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DOI: https://doi.org/10.1007/s10958-023-06677-7