Phase transition at finite temperature in one dimension: Adsorbate ordering in Ba/Si(1 1 1)3 × 2

We demonstrate that the Ba-induced Si(1 1 1)3 × 2 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.