Domino tilings and the six-vertex model at its free fermion point

TL;DR

This paper explores the relationship between domino tilings and the six-vertex model at the free fermion point, revealing phase boundary behaviors described by the Airy process through non-intersecting line mappings.

Contribution

It establishes a detailed mapping between domino tilings and the six-vertex model at the free fermion point using LGV schemes, extending understanding of phase boundaries.

Findings

Boundaries of ordered phases described by the Airy process

Mapping between domino tilings and six-vertex model via non-intersecting lines

Analysis applies to general domains and boundary conditions

Abstract

At the free-fermion point, the six-vertex model with domain wall boundary conditions (DWBC) can be related to the Aztec diamond, a domino tiling problem. We study the mapping on the level of complete statistics for general domains and boundary conditions. This is obtained by associating to both models a set of non-intersecting lines in the Lindstroem-Gessel-Viennot (LGV) scheme. One of the consequence for DWBC is that the boundaries of the ordered phases are described by the Airy process in the thermodynamic limit.