Vector breaking of replica symmetry in some low-temperature disordered systems

We present a new method to study disordered systems in the low-temperature limit. The method uses the replicated Hamiltonian. It studies the saddle points of this Hamiltonian and shows how the various saddle-point contributions can be resummed in order to obtain the scaling behaviour at low temperatures. In a large class of strongly disordered systems, it is necessary to include saddle points of the Hamiltonian which break the replica symmetry in a vector sector, as opposed to the usual matrix sector breaking of the spin glass mean-field theory.