1995/09/25 by Denis Bernard, Bernard, Denis
Physics and Astronomy · #Condensed Matter (cond-mat) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #cond-mat #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9509137
41 pages, latex, uuencoded file with 2 figues included
arxiv created 1995/09/25 · arxiv updated 2009/11/30
We describe applications of (perturbed) conformal field theories to two-dimensional disordered systems. We present various methods of study~: (i) \it A direct method in which we compute the explicit disorder dependence of the correlation functions for any sample of the disorder. This method seems to be specific to two dimensions. The examples we use are disordered versions of the Abelian and non-Abelian WZW models. We show that the disordered WZW model over the Lie group \CG at level k is equivalent at large impurity density to the product of the WZW model over the coset space \CGC/\CG at level (-2hv) times an arbitrary number of copies of the original WZW model. (ii) \it The supersymmetric method is introduced using the random bond Ising model and the random Dirac theory as examples. In particular, we show that the relevent algebra is the affine OSp(2N|2N) Lie superalgebra, an algebra with zero superdimension. (iii) \it The replica method is introduced using the random phase sine-Gordon model as example. We describe particularities of its renormalization group flow. (iv) \it A variationnal approach is also presented using the random phase sine-Gordon model as example. Lectures presented at the '95 Cargese Summer School on "Low dimensional application of quantum field theory".