  Typical quasistatic compression algorithms for generating jammed packings of
athermal, purely repulsive particles begin with dilute configurations and then
apply successive compressions with relaxation of the elastic energy allowed
between each compression step. It is well-known that during isotropic
compression athermal systems with purely repulsive interactions undergo a
jamming transition at packing fraction $\phi_J$ from an unjammed state with
zero pressure to a jammed, rigid state with nonzero pressure. Using extensive
computer simulations, we show that a novel second-order-like transition, the
contact percolation transition, which signals the formation of a
system-spanning cluster of mutually contacting particles, occurs at $\phi_P <
\phi_J$, preceding the jamming transition. By measuring the number of
non-floppy modes of the dynamical matrix, and the displacement field and
time-dependent pressure following compression, we find that the contact
percolation transition also heralds the onset of complex spatiotemporal
response to applied stress. Thus, highly heterogeneous, cooperative, and
non-affine particle motion occurs in unjammed systems significantly below the
jamming transition for $\phi_P < \phi < \phi_J$, not only for jammed systems
with $\phi > \phi_J$.
