Clusters, columns, and lamellae-minimum energy configurations in core softened potentials

We give evidence that particles interacting via the simple, radially symmetric square-shoulder potential can self-organise in highly complex, low-symmetry lattices, thereby forming clusters, columns, or lamellae; only at high pressure are compact, high-symmetry structures observed. Our search for these ordered equilibrium structures is based on ideas of genetic algorithms, a strategy that is characterised by a high success rate. A simple mean-field type consideration complements these findings and locates in a semi-quantitative way the cross-over between the competing structures.