Recently, physical properties of single crystals of quasi-one-dimensional sulfide KCu 7Ϫx S 4 have been studied. These measurements show several anomalies, in which the ''transition'' temperatures and physical properties depend strongly on x. It was suggested that these transitions are most likely due to vacancy ordering involving Cu ϩ -ion diffusion along the Cu͑2͒-Cu͑2͒ zigzag chains. In this paper we propose a long-range mean-field method to study vacancy ordering in a one-dimensional chain with 1/r Coulomb interactions. Our results indicate that phase transitions exist in a one-dimensional lattice gas system in which vacancy ordering is involved. The system has complex thermodynamic properties which are extremely sensitive to the occupancy. Each simple rational occupancy has a unique phase diagram.
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