ROUGHNESS OF CRACK INTERFACES

The width of the crack interface in the fuse model after breakdown, w, scales with the size of the network, L, as omega approximately L-zeta. When the disorder is narrow, or when it includes arbitrarily small threshold values, we find that zeta = 0.7 to within 10%, indicative of this being a universal value. This is not far from 2/3, suggested by an analogy with the random directed polymer problem. When, on the other hand, the disorder is strong and includes arbitrarily large threshold values, the exponent zeta depends on the disorder. These results suggest that the random polymer problem may be relevant for brittle fracture in real materials.