English

On two-point boundary correlations in the six-vertex model with DWBC

Mathematical Physics 2009-11-11 v2 math.MP

Abstract

The six-vertex model with domain wall boundary conditions (DWBC) on an N x N square lattice is considered. The two-point correlation function describing the probability of having two vertices in a given state at opposite (top and bottom) boundaries of the lattice is calculated. It is shown that this two-point boundary correlator is expressible in a very simple way in terms of the one-point boundary correlators of the model on N x N and (N-1) x (N-1) lattices. In alternating sign matrix (ASM) language this result implies that the doubly refined x-enumerations of ASMs are just appropriate combinations of the singly refined ones.

Keywords

Cite

@article{arxiv.math-ph/0503049,
  title  = {On two-point boundary correlations in the six-vertex model with DWBC},
  author = {F. Colomo and A. G. Pronko},
  journal= {arXiv preprint arXiv:math-ph/0503049},
  year   = {2009}
}

Comments

v2: a reference added, typos corrected

R2 v1 2026-07-22T16:25:48.313Z