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

Patrik L. Ferrari·Herbert Spohn
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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.

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Patrik L. Ferrari, Herbert Spohn. 2006-05-16. Domino tilings and the six-vertex model at its free fermion point. https://doi.org/10.1088/0305-4470%2F39%2F33%2F003

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