Amorphous Order and Nonlinear Susceptibilities in Glassy Materials.

We review 15 years of theoretical and experimental work on the nonlinear response of glassy systems. We argue that an anomalous growth of the peak value of nonlinear susceptibilities is a signature of growing "amorphous order" in the system, with spin-glasses as a case in point. Experimental results on supercooled liquids are fully compatible with the random first-order transition (RFOT) prediction of compact "glassites" of increasing volume as temperature is decreased, or as the system ages. We clarify why such a behavior is hard to explain within purely kinetic theories of glass formation, despite recent claims to the contrary.