Multiphase behaviour of the plane quadratic lattice gas with nearest-neighbour exclusion and next-nearest-neighbour finite interaction

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Abstract
The plane quadratic lattice gas with nearest-neighbour exclusion and next-nearest-neighbour finite interaction is considered in the framework of the double-site and single-square approximations of the cluster variation method and in the branched lattice approximation. In addition to the disordered and hard-core-ordered phases only one extra phase is shown to exist which arises at low temperatures near the half-maximum density. This phase which is due to the next-nearest-neighbour repulsion exhibits both first- and second-order transitions to the disordered phase.