Existence of isostatic, maximally random jammed monodisperse hard-disk packings

Disordered particle packings are ubiquitous in all areas of science. Although disordered jammed packings of hard spheres are readily observed in 3D, the story is quite different for disks. Most 2D packing protocols tend to produce highly ordered disk arrangements, suggesting that truly disordered jammed disk packings might not exist in 2D. The maximally random jammed (MRJ) configurations we observe have a complete lack of crystallinity and are distinct from the typical jammed configuration that is most probable upon rapid compression. A protocol-independent geometric-structure approach allows us to create, identify, and analyze these previously elusive packings. Our results shed new light on the nature of randomness, which is an issue that arises across the physical, mathematical, and biological sciences.