Infrared singularities in d≤2 disordered interacting systems

We address the problem of infrared singularities in the perturbation theory for disordered interacting systems in d less than or equal to 2. We show that a typical sufficiently large interacting system exhibits a linear instability in-the spin-triplet channel. In the density-density channel, although stability is preserved, a large number of soft modes is accumulated. These phenomena are responsible for the instability of the weak-interacting fixed point. Although generic, the unstable direction and soft modes are highly sample specific and cannot be effectively captured by conventional techniques;based on an averaging procedure. Rather, the instability is determined by the largest eigenvalues of the polarization operator. We propose to employ the optimal-fluctuation method for evaluating the probability of such events.