  The self-dual random-bond eight-state Potts model is studied numerically
through large-scale Monte Carlo simulations using the Swendsen-Wang cluster
flipping algorithm. We compute bulk and surface order parameters and
susceptibilities and deduce the corresponding critical exponents at the random
fixed point using standard finite-size scaling techniques. The scaling laws are
suitably satisfied. We find that a belonging of the model to the 2D Ising model
universality class can be conclusively ruled out, and the dimensions of the
relevant bulk and surface scaling fields are found to take the values
$y_h=1.849$, $y_t=0.977$, $y_{h_s}=0.54$, to be compared to their Ising values:
15/8, 1, and 1/2.
