  We study the local height probabilities in a composite height model, derived
from the restricted solid-on-solid model introduced by Andrews, Baxter and
Forrester, and their connection with conformal field theory characters. The
obtained conformal field theories also describe the critical behavior of the
model at two different critical points. In addition, at criticality, the model
is equivalent to a one-dimensional chain of anyons, subject to competing two-
and three-body interactions. The anyonic-chain interpretation provided the
original motivation to introduce the composite height model, and by obtaining
the critical behaviour of the composite height model, the critical behaviour of
the anyonic chains is established as well. Depending on the overall sign of the
hamiltonian, this critical behaviour is described by a diagonal coset-model,
generalizing the minimal models for one sign, and by Fateev-Zamolodchikov
parafermions for the other.
