Boundary correlation functions of the six-vertex model

TL;DR

This paper derives determinant formulas for boundary correlation functions in the six-vertex model with domain wall boundary conditions, providing explicit solutions in the free fermion case and linking to combinatorial enumeration problems.

Contribution

It generalizes known results for the partition function to boundary correlation functions and explicitly solves the free fermion case, connecting statistical mechanics with combinatorics.

Findings

Boundary correlation functions expressed as determinants

Explicit solutions obtained in the free fermion case

Connections established with alternating sign matrices and domino tilings

Abstract

We consider the six-vertex model on an $N \times N$ square lattice with the domain wall boundary conditions. Boundary one-point correlation functions of the model are expressed as determinants of $N\times N$ matrices, generalizing the known result for the partition function. In the free fermion case the explicit answers are obtained. The introduced correlation functions are closely related to the problem of enumeration of alternating sign matrices and domino tilings.