Jamming Transition: Soft Sphere Packing

The jamming transition (Point J) occurs when athermal soft spheres are compressed to a packing fraction φ_J ≈ 0.64 in 2D. Below J, spheres rattle freely; above J, they form a rigid amorphous solid with power-law contact forces. The transition is characterized by diverging length scales and a sudden onset of rigidity.