The reconstruction transitions on certain clean metal surfaces were shown to be isomorphic with two-dimensional models of phase transitions. Specifically, the Pt, Ir, and Au(110) transitions corresponded to the 2d-Ising model, the W(100) transition to the 2d−XY model with cubic anisotropy. The Mo (100) reconstruction was described in terms of the Kosterlitz-Thouless picture of the 2d-XY model. Experiments (low-energy electron diffraction or He diffraction) were suggested to check theories of 2d systems.

Surface Reconstruction - a Physical Realization of Two-Dimensional Ising and XY-Models. P.Bak: Solid State Communications, 1979, 32[7], 581-3