The absence of a liquid phase in van der Waals fluids at high dimensionality

It is demonstrated that a model van der Waals fluid does not possess a liquid phase at high dimensionality. The model is hard hypercubes with a long-range attraction. The gas-liquid and fluid-solid transitions cross as the dimensionality is increased, and at high dimensionality the gas-liquid transition is pre-empted by the transition to a solid phase.