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

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

2006-05-16

arxiv.org/abs/cond-mat/0605406v1

J. Phys. A: Math. Gen. 39 (2006), 10297-10306

Physics

Condensed Matter

Statistical Mechanics

14 pages, 8 figures

Scientific paper

10.1088/0305-4470/39/33/003

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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