Two-dimensional lattice liquids

Evidence is presented, based on transfer-matrix and Monte Carlo calculations, for the occurrence of a gas-liquid phase transition in suitably constructed, two-dimensional lattice-gas models with extended hard-core repulsion on the triangular lattice. Three different models having this property are identified. The first system is characterized by nearest-neighbor exclusion and an interparticle attraction ranging from second- to fourth-neighbor distance. In a further example, the hard core reaches second neighbors, while the attraction ranges from third to fifth neighbors. Finally, in a third model, the core extends up to fourth neighbors, while the attraction covers all distances from fifth to eighth neighbors. I discuss how to use these results in order to make a realistic lattice simulation of the triangular, (111) surface of a fcc solid.