  Using Monte Carlo techniques and a star-triangle transformation, Ising models
with random, 'strong' and 'weak', nearest-neighbour ferromagnetic couplings on
a square lattice with a (1,1) surface are studied near the phase transition.
Both surface and bulk critical properties are investigated. In particular, the
critical exponents of the surface magnetization, 'beta_1', of the correlation
length, 'nu', and of the critical surface correlations, 'eta_{\parallel}', are
analysed.
