  We present a universal characterization of stress correlations in athermal
systems, across crystalline to amorphous packings. Via numerical analysis of
static configurations of particles interacting through harmonic as well as
Lennard-Jones potentials, for a variety of preparation protocols and ranges of
microscopic disorder, we show that the properties of the stress correlations at
large lengthscales are surprisingly universal across all situations,
independent of structural correlations, or the correlations in orientational
order. In the near-crystalline limit, we present exact results for the stress
correlations for both models, which work surprisingly well at large
lengthscales, even in the amorphous phase. Finally, we study the differences in
stress fluctuations across the amorphization transition, where stress
correlations reveal the loss of periodicity in the structure at short
lengthscales with increasing disorder.
