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

Abstract

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