  We derive exact results for the fluctuations in energy produced by
microscopic disorder in near-crystalline athermal systems. Our formalism
captures the heterogeneity in the elastic energy of polydispersed soft disks in
energy-minimized configurations. We use this to predict the distribution of
interaction energy between two defects in a disordered background. We show this
interaction energy displays an average power-law behaviour $\langle \delta E
\rangle \sim \Delta^{-4}$ at large distances $\Delta$ between the defects.
These interactions upon disorder average also display the sixfold symmetry of
the underlying reference crystal. Additionally, we show that the fluctuations
in the interaction energy encode the athermal correlations introduced by the
disordered background. We verify our predictions with energy minimized
configurations of polydispersed soft disks in two dimensions.
