c-Theorem for Disordered Systems

Details c-Theorem for Disordered Systems c-Theorem for Disordered Systems

1998-08-07

arxiv.org/abs/cond-mat/9808063v1

Nucl.Phys. B546 (1999) 765

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages

Scientific paper

10.1016/S0550-3213(99)00013-9

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.

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