Parafermionic excitations and critical exponents of random cluster and O(n) models

We introduce the notion of parafermionic fields as the chiral fields which describe particle excitations in two-dimensional conformal field theory, and argue that the parafermionic conformal dimensions can be determined using scale invariant scattering theory. Together with operator product arguments this may provide new information, in particular for non-rational conformal theories. We obtain in this way the field theoretical derivation of the critical exponents of the random cluster and O(n) models, which in the limit of vanishing central charge yield percolation and self-avoiding walks. A simple derivation of the relation between S-matrix and Lagrangian couplings of sine-Gordon model is also given. (C) 2013 Elsevier Inc. All rights reserved.