Disordered Systems and Logarithmic Conformal Field Theory

M. Reza Rahimi Tabar

Disordered Systems and Logarithmic Conformal Field Theory

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arxiv cond-mat/0111327 v2 pith:A7M4P2PU submitted 2001-11-19 cond-mat hep-th

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keywords conformalfieldlogarithmictheorydisorderedlcftsystemscorrelation

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abstract

We review a recent development in theoretical understanding of the quenched averaged correlation functions of disordered systems and the logarithmic conformal field theory (LCFT) in d-dimensions. The logarithmic conformal field theory is the generalization of the conformal field theory when the dilatation operator is not diagonal and has the Jordan form. It is discussed that at the random fixed point the disordered systems such as random-bond Ising model, Polymer chain, etc. are described by LCFT and their correlation functions have logarithmic singularities. As an example we will discuss in detail the application of LCFT to the problem of random-bond Ising model in $ 2 \leq d \leq 4$.

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The bulk energy four-point function in percolation and self-avoiding walk CFTs is non-zero at c=0, driven by coupling to a rank-3 Jordan block associated with the second energy operator.

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