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Boundary polarization in the six-vertex model

N. M. Bogoliubov·A. V. Kitaev·M. B. Zvonarev
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Abstract

Vertical-arrow fluctuations near the boundaries in the six-vertex model on the two-dimensional $N \times N$ square lattice with the domain wall boundary conditions are considered. The one-point correlation function (`boundary polarization') is expressed via the partition function of the model on a sublattice. The partition function is represented in terms of standard objects in the theory of orthogonal polynomials. This representation is used to study the large N limit: the presence of the boundary affects the macroscopic quantities of the model even in this limit. The logarithmic terms obtained are compared with predictions from conformal field theory.

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N. M. Bogoliubov, A. V. Kitaev, M. B. Zvonarev. 2002-01-21. Boundary polarization in the six-vertex model. https://doi.org/10.1103/physreve.65.026126

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