Absence of the liquid phase when the attraction is not pairwise additive

Recent work on charged colloidal suspensions with very low levels of added salt has suggested that although pairs of the colloidal particles repel, clusters of the particles attract. Motivated by this, we study simple model particles which have many-body attractions. These attractions are generic many-body attractions and are not calculated for any specific colloidal suspension. We find that many-body attractions can stabilize solid phases at low pressures but that the liquid phase is either completely absent from the equilibrium phase diagram or present only within a small region of parameter space.