Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications

Understand

We describe an approach to logarithmic conformal field theories as limits of sequences of ordinary conformal field theories with varying central charge c.

• Logarithmic behaviour arises from degeneracies in the spectrum of scaling dimensions at certain values of c.
• The theories we consider are all invariant under some internal symmetry group, and logarithmic behaviour occurs when the decomposition of the physical observables into irreducible operators becomes singular.
• Examples considered are quenched random magnets using the replica formalism, self-avoiding walks as the n->0 of the O(n) model, and percolation as the limit Q->1 of the Potts model.