We present phase diagrams showing the stable phases of a two-dimensional lattice gas. The molecules reside on the triangular lattice and have hard cores which exclude other molecules from the first-and second-neighbor positions. An interaction w (positive or negative) is postulated for molecules separated by the third-neighbor distance, and no interaction is experienced at still greater separation. For attractive third-neighbor interactions (negative 10) the phase diagram possesses only two regions: solid and fluid. The transition between them is first order at all temperatures, but more strongly first order at low temperatures. For positive 10 (soft repulsions), the phase diagram is topologically similar to that of helium. In addition to a solid region and a gaseous region, there are areas identified as a "normal liquid" and an "ordered liquid," the latter being the stable phase as T--'O at moderate pressures.
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