  The two-dimensional random-bond Ising model is numerically studied on long
strips by transfer-matrix methods. It is shown that the rate of decay of
correlations at criticality, as derived from averages of the two largest
Lyapunov exponents plus conformal invariance arguments, differs from that
obtained through direct evaluation of correlation functions. The latter is
found to be, within error bars, the same as in pure systems. Our results
confirm field-theoretical predictions. The conformal anomaly $c$ is calculated
from the leading finite-width correction to the averaged free energy on strips.
Estimates thus obtained are consistent with $c=1/2$, the same as for the pure
Ising model.
