The pressure-induced diatomic-to-monatomic phase transition is investigated in a model crystal based on a Tersoff-type interatomic potential. The phase transition is first-order when the many-body interaction is long-ranged, but second-order when the many-body interaction is short-ranged. The change in the order of the phase transition is related to a crossing of the stability limits of the diatomic structure with respect to fluctuations of volume and with respect to fluctuations of the internal parameter.