Large-scale exponential correlations of nonaffine elastic response of strongly disordered materials
The correlation properties of the nonaffine elastic response in strongly disordered materials are investigated using the theory of correlated random matrices and supported by numerical models. While the nonaffine displacement field itself predominantly exhibits power-law decay, we demonstrate that its spatial derivatives reveal large-scale exponentially decaying correlations. Specifically, the correlation functions of the divergence and (for most deformations) the rotor of the nonaffine field are governed by a heterogeneity length scale $ξ$. This length scale is set by the disorder strength and can become indefinitely large, far exceeding the structural correlation length. A notable exception occurs under volumetric deformation, where the rotor correlations lack the exponential tail with the length scale $ξ$. The theory also predicts that the rotor correlations may have small power-law tails. We directly observe the exponential decay, characterized by $ξ$, in numerical studies of a rigidity percolation model and in molecular dynamics simulations of amorphous polystyrene and the Lennard-Jones glass. The latter example also confirms the existence of the power-law tail in the rotor correlation function at large distances.