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

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.

v2: a reference added, typos corrected

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• A doubly-refined enumeration of alternating sign matrices and descending plane partitions
• The 6-vertex model with fixed boundary conditions
• The frustration-free fully packed loop model
• Six-vertex model on a finite lattice: integral representations for nonlocal correlation functions
• Generalized emptiness formation probability in the six-vertex model
• Coupled Fredkin and Motzkin chains from quantum six- and nineteen-vertex models
• Free fermions in classical and quantum integrable models
• Doubly-refined enumeration of Alternating Sign Matrices and determinants of 2-staircase Schur functions
• Factorization in the multirefined tangent method
• More refined enumerations of alternating sign matrices
• A formula for the doubly-refined enumeration of alternating sign matrices
• Linear relations of refined enumerations of alternating sign matrices