Solids between the mechanical extremes of order and disorder

For more than a century, physicists have described real solids in terms of perturbations about perfect crystalline order1. Such an approach takes us only so far: a glass, another ubiquitous form of rigid matter, cannot be described in any meaningful sense as a defected crystal2. Is there an opposite extreme to a crystal—a solid with complete disorder—that forms an alternative starting point for understanding real materials? Here, we argue that the solid comprising particles with finite-ranged interactions at the jamming transition3,4,5 constitutes such a limit. It has been shown that the physics associated with this transition can be extended to interactions that are long ranged6. We demonstrate that jamming physics is not restricted to amorphous systems, but dominates the behaviour of solids with surprisingly high order. Just as the free-electron and tight-binding models represent two idealized cases from which to understand electronic structure1, we identify two extreme limits of mechanical behaviour. Thus, the physics of jamming can be set side by side with the physics of crystals to provide an organizing structure for understanding the mechanical properties of solids over the entire spectrum of disorder.