Correlation between Voronoi volumes in disc packings

We measure the two-point correlation of free Voronoi volumes in binary disc packings, where the packing fraction ϕ avg ranges from 0.8175 to 0.8380. We observe short-ranged correlations over the whole range of ϕ avg and anticorrelations for ϕ avg > 0.8277. The spatial extent of the anti-correlation increases with ϕ avg while the position of the maximum of the anticorrelation and the extent of the positive correlation shrink with ϕ avg . We conjecture that the onset of anticorrelation corresponds to dilatancy onset in this system.