Geometric signatures of jamming in the mechanical vacuum

Jamming has traditionally been studied as a mechanical phenomenon and characterized with mechanical order parameters. However, this approach is not meaningful in the "mechanical vacuum" of systems below jamming in which all mechanical properties are precisely zero. We find that the network of nearest neighbors and the geometric structure of the Voronoi cell contain well-defined and meaningful order parameters for jamming, which exist on both sides of the transition. We observe critical exponents in these order parameters and an upper critical dimension of 3. Further, we present evidence for a new incipient-jamming phase below the jamming transition marked by additional symmetry in the Voronoi tessellation.