Nonequilibrium static diverging length scales on approaching a   prototypical model glassy state
  Maximally random jammed states of hard spheres are prototypical glasses. We study the small wavenumber $k$ behavior of the structure factor $S(k)$ of overcompressed million-sphere packings as a function of density up to the jammed state. We find both a precursor to the glassy jammed state evident long before the jamming density is reached and an associated growing length scale, extracted from the volume integral of the direct correlation function $c(r)$, which diverges at the "critical" jammed state. We also define a nonequilibrium index $X$ and use it to demonstrate that the packings studied are intrinsically nonequilibrium in nature well before the critical point is reached. 
Adam B. Hopkins, Frank H. Stillinger, and Salvatore Torquato
cond-mat.stat-mech cond-mat.soft math-ph math.MP