c-Theorem for Disordered Systems
arXiv:cond-mat/9808063 · doi:10.1016/S0550-3213(99)00013-9
Abstract
We find an analog of Zamolodchikov's c-theorem for disordered two dimensional noninteracting systems in their supersymmetric representation. For this purpose we introduce a new parameter b which flows along the renormalization group trajectories much like the central charge for unitary two dimensional field theories. However, it is not known yet if this flow is irreversible. b turns out to be related to the central extension of a certain algebra, a generalization of the Virasoro algebra, which we show may be present at the critical points of these theories. b is also related to the physical free energy of the disordered system defined on a cylinder. We discuss possible applications by computing b for two dimensional Dirac fermions with random gauge potential.
7 pages