One-Point Function of the Four-Vertex Model

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...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-09, Vol.275 (3), p.249-258
Main Authors: Bogolyubov, N. M., Pronko, A. G.
Format: Article
Language:English
Subjects:
Antiferroelectricity
Boundary conditions
Mathematics
Mathematics and Statistics
Order parameters
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06677-7