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 wit h a long-range attraction. The gas-liquid and fluid-solid transitions cross as the dimensionality is increased, and at high dimensionality t he gas-liquid transition is pre-empted by the transition to a solid ph ase.