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Mechanical Yield in Amorphous Solids: a First-Order Phase Transition

Amorphous solids yield at a critical value of the strain (in strain controlled experiments); for larger strains the average stress can no longer increase - the system displays an elasto-plastic steady state. A long standing riddle in the materials community is what is the difference between the microscopic states of the material before and after yield. Explanations in the literature are material specific, but the universality of the phenomenon begs a universal answer. We argue here that there is no fundamental difference in the states of matter before and after yield, but the yield is a bona-fide first order phase transition between a highly restricted set of possible configurations residing in a small region of phase space to a vastly rich set of configurations which include many marginally stable ones. To show this we employ an order parameter of universal applicability, independent of the microscopic interactions, that is successful in quantifying the transition in an unambiguous manner.