  We consider the critical behavior of two-dimensional Potts models in presence
of a bond disorder in which the correlation decays as a power law. In some
recent work the thermal sector of this theory was investigated by a
renormalization group computation based on perturbed conformal field theory.
Here we apply the same approach to study instead the magnetic sector. In
particular we compute the leading corrections to the Potts spin scaling
dimension. Our results include as a special case the long-range disorder Ising
model. We compare our prediction to Monte-Carlo simulations. Finally, by
studying the magnetization scaling function, we show a clear numerical evidence
of a cross-over between the long-range and the short-range class of
universality.
