Journal of Statistical Physics, Vol. 95, Nos. 34, 1999, p. 759-766.
We consider two-dimensional Ising models with randomly distributed ferromagnetic bonds and study the local critical behavior at defect lines by extensive Monte Carlo simulations. Both for ladder- and chain-type defects, nonuniversal critical behavior is observed: the critical exponent of the defect magnetization is found to be a continuous function of the strength of the defect coupling. Analyzing corresponding stability conditions, we obtain new evidence that the critical exponent v of the bulk correlation length of the random Ising model does not depend on dilution, i.e., v=l.