  Inferring the nature of disorder in the media where elastic objects are
nucleated is of crucial importance for many applications but remains a
challenging basic-science problem. Here we propose a method to discern whether
weak-point or strong-correlated disorder dominates based on characterizing the
distribution of the interaction forces between objects mapped in large
fields-of-view. We illustrate our proposal with the case-study system of vortex
structures nucleated in type-II superconductors with different pinning
landscapes. Interaction force distributions are computed from individual vortex
positions imaged in thousands-vortices fields-of-view in a
two-orders-of-magnitude-wide vortex-density range. Vortex structures nucleated
in point-disordered media present Gaussian distributions of the interaction
force components. In contrast, if the media have dilute and
randomly-distributed correlated disorder, these distributions present
non-Gaussian algebraically-decaying tails for large force magnitudes. We
propose that detecting this deviation from the Gaussian behavior is a
fingerprint of strong disorder, in our case originated from a dilute
distribution of correlated pinning centers.
