A novel field theoretical approach to the Anderson localization : sparse random hopping model

We develop a novel supersymmetric field-theoretical model describing a motion of a particle in a system with long range percolative type off-diagonal disorder. The model is investigated in a saddle point approximation. The delocalization transition manifests itself as spontaneous breaking of a symmetry of the effective Lagrangian. Both phases of the system can be described by means of an orderparameter function having a clear physical meaning related to statistical properties of Green functions. We calculate the inverse participation ratio and correlation functions in both localized and extended phases. The found critical behaviour agrees with results obtained in the framework of effective medium approximation for the supermatrix σ-model. Some speculations about the value of upper critical dimension consistent with the obtained results are put forward.