  What characterises a solid is its way to respond to external stresses.
Ordered solids, such crystals, display an elastic regime followed by a plastic
one, both well understood microscopically in terms of lattice distortion and
dislocations. For amorphous solids the situation is instead less clear, and the
microscopic understanding of the response to deformation and stress is a very
active research topic. Several studies have revealed that even in the elastic
regime the response is very jerky at low temperature, resembling very much the
one of disordered magnetic materials. Here we show that in a very large class
of amorphous solids this behaviour emerges by decreasing the temperature as a
phase transition where standard elastic behaviour breaks down. At the
transition all non-linear elastic modulii diverge and standard elasticity
theory does not hold anymore. Below the transition the response to deformation
becomes history and time-dependent.
