Phase Transitions in Two-Dimensional Lattice Gases of Hard-Core Molecules. The Triangular Lattice

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Abstract
The thermodynamic properties of assemblies of molecules with a hard core on a triangular lattice have been investigated by the matrix method and by series expansions. Three particular cases have been considered (denoted as B, C, D), corresponding, respectively, to exclusion ranges extending up to second‐, third‐, and fourth‐neighboring sites. Case A (i.e., exclusion on first‐neighboring sites only) has been studied previously by other authors, who concluded to the existence of a second‐order continuous transition at high density. For all three cases B, C, and D, there is a good evidence for a first‐order phase change of the fluid–solid type, similar to the transition observed for hard disks and hard spheres.