As temperature is lowered, motion becomes more sluggish. Below the glass transition temperature, the dynamics of super-cooled liquids becomes so slow that the system falls out of equilibrium. One hypothesis for this dynamic arrest is that it is due to a thermodynamic phase transition with a diverging length scale. However, there is scant evidence of such a length scale appearing in the structure. Motivated by this, we study another amorphous system that undergoes a phase transition: jammed soft repulsive spheres at zero temperature. We have discovered a subtle correlation length, associated with the local coordination of particles, that is not seen in the two-point correlation function, g(r). We argue that this scale plays an important role in determining the local rigidity of the system, and diverges with an exponent 2/(d+1) as the jamming transition is approached.
