Perturbed Conformal Field Theory Applied to 2D Disordered Systems: AnIntroduction

摘要

The authors describe applications of (perturbed) conformal field theories to two-dimensional disordered systems. The authors present various methods of study: (1) A direct method in which the authors compute the explicit disorder dependence of the correlation function for any sample of the disorder. This method seems to be specific to two dimensions; (2) The supersymmetric method is introduced using the random bond Ising model and the random Dirac theory as examples. In particular, the authors show that the relevant algebra is the affine OSp(2N/2N) Lie superalgebra, an algebra with zero superdimension; (3) The replica method is introduced using the random phase sine-Gordon model as example. The authors describe particularities of its renormalization group flow. (4) A variationnal approach is also presented using the random phase sine-Gordon model as example.