Disordered Systems and Logarithmic Conformal Field Theory

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 $2\le d\le 4$.

47 pages, latex, to appear in Int. J. of Mod. Phys. A (2003)

References in corpus (3)

• Modular transformation and boundary states in logarithmic conformal field theory
• World Sheet Logarithmic CFT in AdS Strings, Ghost-Matter Mixing and M-theory
• Prelogarithmic operators and Jordan blocks in SL(2)_k affine algebra

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• A note on the identity module in $c=0$ CFTs
• Extended chiral algebras and the emergence of SU(2) quantum numbers in the Coulomb gas
• The origin of multiplets of chiral fields in SU(2)_k WZNW at rational level
• Logarithmic operators in $c=0$ bulk CFTs