Ising models with nearest neighbor ferromagnetic random couplings on a
square lattice with a (1, 1) surface are studied, using Monte Carlo t
echniques and a star-triangle transformation method. In particular, th
e critical exponent of the surface magnetization is found to be close
to that of the perfect model, beta(1) = 1/2. The crossover from surfac
e to bulk critical properties is discussed.