  Amorphous solids increase their stress as a function of an applied strain
until a mechanical yield point whereupon the stress cannot increase anymore,
afterwards exhibiting a steady state with a constant mean stress. In stress
controlled experiments the system simply breaks when pushed beyond this mean
stress. The ubiquity of this phenomenon over a huge variety of amorphous solids
calls for a generic theory that is free of microscopic details. Here we offer
such a theory: the mechanical yield is a thermodynamic phase transition, where
yield occurs as a spinodal phenomenon. At the spinodal point there exists a
divergent correlation length which is associated with the system-spanning
instabilities (known also as shear bands) which are typical to the mechanical
yield. The theory, the order parameter used and the correlation functions which
exhibit the divergent correlation length are universal in nature and can be
applied to any amorphous solids that undergo mechanical yield.

Disordered Systems and Neural Networks