Abstract

The ground state of the triangular lattice gas model with up to 3rd neighbor interactions is investigated by use of the method of geometrical inequalities. The structure of the ground state at an arbitrary value of the particle density is determined in the full regimes of the interactions. Various ordered structures are obtained. Several examples of systems of adsorbates on the FCC(111) plane, of interstitial atoms in the transition metal carbides and nitrides and of the Ising spins, which may correspond to the present model, are discussed on the basis of the obtained results. A certain amount of information about the interactions in the systems is deduced from the observed ordered structures.

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