A diverging length scale in the structure of jammed systems

Super-cooled liquids undergo an enormous slowing down of their dynamics when their temperature is lowered towards the glass transition. Despite the huge growth in time scale there appears to be little change in the structure. This has prompted the suggestion that there is a hidden form of ordering. Motivated by this, we study another amorphous system that undergoes a phase transition into a rigid state: jammed soft repulsive spheres at zero temperature. We have discovered a subtle structural ordering, not seen in the two-point correlation function, g(r), that is associated with the coordination of particles [1]. On scales below a length scale that diverges at the jamming point, the contact fluctuations are sub-extensive (hyperuniform). We argue that this length scale diverges with an exponent 2/(d+1) as the jamming transition is approached.
[1] arXiv:1710.07317