Phase transition at finite temperature in one dimension: Adsorbate   ordering in Ba/Si(111)3x2
  We demonstrate that the Ba-induced Si(111)3x2 reconstruction is a physical realization of a one-dimensional antiferromagnetic Ising model with long-range Coulomb interactions. Monte Carlo simulations performed on a corresponding Coulomb-gas model, which we construct based on density-functional calculations, reveal an adsorbate-ordering phase transition at finite temperature. We show numerically that this unusual one-dimensional phase transition should be detectable by low-energy electron diffraction. 
Steven C. Erwin and C. Stephen Hellberg