We explain how a quantum version of the cavity method can be used to describe the quantum phase transitions in low temperature, strongly disordered, ferromagnets and superconductors. At variance with the usual quantum critical points, we find a phase diagram with two critical points separating three phases. When the disorder increases, the systems goes from the ordered phase to an intermediate disordered phase characterized by activated transport and then to a second disordered phase where no transport is possible. Both the ordered and disordered phases exhibit strong inhomogeneity of their basic properties typical of glassy physics. These properties are studied analytically through a mapping to directed polymers in random medium on a tree.

LPTMS, Orsay