Boundary polarization in the six-vertex model
Statistical Mechanics
2009-11-07 v3 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
Vertical-arrow fluctuations near the boundaries in the six-vertex model on the two-dimensional 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.
Cite
@article{arxiv.cond-mat/0107146,
title = {Boundary polarization in the six-vertex model},
author = {N. M. Bogoliubov and A. V. Kitaev and M. B. Zvonarev},
journal= {arXiv preprint arXiv:cond-mat/0107146},
year = {2009}
}
Comments
4 pages, RevTex, a misprint in Eq. (8) is corrected