Disorder-induced roughening in the three-dimensional Ising model

Using an exact method, we numerically study the zero-temperature roughness of interfaces in the random bond, cubic lattice, Ising model (of size L³, with $L<~80$). Interfaces oriented along the {100} direction undergo a roughening transition from a weak disorder phase, which is almost flat, to a strong disorder phase with interface width w~cL0.42 (c is a function of the disorder). For random dilution we find the roughening threshold p*=0.89±0.01 and c~p*-p for p<~p* (p is the volume fraction of present bonds). In contrast {111} interfaces are algebraically rough for all disorder.