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

TL;DR

This paper derives a simple expression for the two-point boundary correlation function in the six-vertex model with DWBC, linking it to one-point correlators and revealing combinatorial implications for alternating sign matrices.

Contribution

It provides a novel, simple formula connecting two-point and one-point boundary correlators in the six-vertex model with DWBC.

Findings

Two-point boundary correlator expressed via one-point correlators.

Doubly refined ASM enumerations are combinations of singly refined ones.

Simplifies understanding of boundary correlations in the model.

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.