The Aztec diamond of order n is a checkerboard region. A uniformly random domino tiling of this region exhibits a spectacular phase transition: the interior of an inscribed circle is chaotic ("temperate zone"), while the four corners are frozen — each covered by dominoes aligned in a single direction.
The four colors show the four domino orientations: N/S/E/W. The frozen corners use only one orientation. The circle boundary is sharp in the thermodynamic limit — a genuine phase boundary between ordered and disordered phases.
This connects to random matrices (GUE), non-intersecting lattice paths, the KPZ universality class, and the Airy process at the boundary.