Multiscaling at Point J: Jamming is a Critical Phenomenon

Abstract

We analyze the jamming transition that occurs as a function of increasing packing density in a disordered two-dimensional assembly of disks at zero temperature for ``Point J'' of the recently proposed jamming phase diagram. We measure the total number of moving disks and the transverse length of the moving region, and find a power law divergence as the packing density increases toward a critical jamming density. This provides evidence that the T = 0 jamming transition as a function of packing density is a {\it second order} phase transition. Additionally we find evidence for multiscaling, indicating the importance of long tails in the velocity fluctuations.