Experiments using band-excitation scanning probe microscopy at DOE's Oak Ridge National Laboratory are providing clues to the origins of unique properties of spin and cluster glasses, phase-separated oxides, polycrystalline ferroelectrics and ferromagnets that are rooted in their highly disordered structure. Studies with the new analytic method, reported in Proceedings of the National Academy of Sciences, showed that hysteresis in these nanoscale materials is directly related to the collective behavior of their disordered structures. These behaviors influence the size of the material such as the thickness of a thin film at which improved properties manifest. So-called "Rayleigh behaviors" and their unpredictability have a direct bearing on the ability to fabricate nanoscale materials and, eventually, to make nanoscale devices. The new observations, which were made possible by advances in scanning probe microscopy at ORNL's Center for Nanophase Materials Sciences, may result in the rethinking of 100-year-old theories behind the "quanta of nonlinearity" and properties of disordered materials. This work is funded by DOE Basic Energy Sciences CNMS user program. PIs are Stephen Jesse and Sergei Kalinin.