On the Nature of Infrared Singularities in $d\leq 2$ Disordered Interacting Systems

Details On the Nature of Infrared Singularities in $d\leq 2$ Disordered Interacting Systems On the Nature of Infrared Singularities in $d\leq 2$ Disordered Interacting Systems

1997-10-10

arxiv.org/abs/cond-mat/9710093v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, RevTeX. References added, minor changes

Scientific paper

10.1103/PhysRevB.58.5149

We address the problem of infrared singularities in the perturbation theory for disordered interacting systems in $d\leq 2$. We show that a typical, sufficiently large interacting system exhibits a linear instability in the spin triplet channel. In a 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 can not 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.

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