On two-point boundary correlations in the six-vertex model with domain wall boundaryconditions

Abstract

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