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. In these cases we identify logarithmic
operators and pay particular attention to how the c->0 paradox is resolved and
how the b-parameter is evaluated. We also show how this approach gives
information on logarithmic behaviour in the extended Ising model, uniform
spanning trees and the O(-2) model. Most of our results apply to general
dimensionality. We also consider massive logarithmic theories and, in two
dimensions, derive sum rules for the effective central charge and the
b-parameter.Comment: 37 pages. v2: minor corrections and additions. Submitted to Special
Issue of J. Phys. A on Logarithmic CF
