Microscopic View of a Two-Dimensional Lattice-Gas Ising System within the Grand Canonical Ensemble

A reversible 2D critical transition is observed on the GaAs(001) surface and modeled as a lattice-gas Ising system. Without depositing any material, 2D GaAs islands spontaneously form. The order parameter, four critical exponents, and coupling energies are measured from scanning tunneling microscope images of the microscopic domain structure and correlation functions as a function of temperature and pressure. Unprecedented insight into the domain structure of a 2D Ising system through the critical point and a complete Hamiltonian for modeling the GaAs(001) surface are presented.