We show the existence of compactly supported global minimisers under almost optimal hypotheses for continuum models of particles interacting through a potential. The main assumption on the potential is that it is catastrophic - the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the "gaps'' it may have. If moreover the potential is smooth at the origin, we prove that minimisers have discrete and finite support. Joint works with J. A. Cañizo, J. A. Carrillo and A. Figalli.