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

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

2005-03-21

arxiv.org/abs/math-ph/0503049v2

J.Stat.Mech. 0505 (2005) P05010

Physics

Mathematical Physics

v2: a reference added, typos corrected

Scientific paper

10.1088/1742-5468/2005/05/P05010

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.

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