  We explore the properties of the low-temperature phase of the O($n$) loop
model in two dimensions by means of transfer-matrix calculations and
finite-size scaling. We determine the stability of this phase with respect to
several kinds of perturbations, including cubic anisotropy, attraction between
loop segments, double bonds and crossing bonds. In line with Coulomb gas
predictions, cubic anisotropy and crossing bonds are found to be relevant and
introduce crossover to different types of behavior. Whereas perturbations in
the form of loop-loop attractions and double bonds are irrelevant, sufficiently
strong perturbations of these types induce a phase transition of the Ising
type, at least in the cases investigated. This Ising transition leaves the
underlying universal low-temperature O($n$) behavior unaffected.
