  Plasticity in amorphous solids is mediated by localized quadrupolar
instabilities, but the mechanism by which an amorphous solid eventually fails
or melts is debated. In this work we argue that these phenomena can be
investigated in the model problem of an elastic continuum with quadrupolar
defects, at finite temperature. This problem is posed and the collective
behavior of the defects is analytically investigated. Using both
renormalization group and field-theoretic techniques, it is found that the
model has a yielding/melting transition of spinodal type.
