QUASI-STATIC CRACKS AND MINIMAL ENERGY SURFACES

We compare the roughness of minimal energy (ME) surfaces and scalar '' quasistatic'' fracture (SQF) surfaces. Two-dimensional ME and SQF surf aces have the same roughness scaling, w similar to L-zeta (L is the sy stem size) with zeta = 2/3. The 3d ME and SQF results at strong disord er are consistent with the random-bond Ising exponent zeta(d greater t han or equal to 3) approximate to 0.21 (5 - d) (d is the bulk dimensio n). However, 3d SQF surfaces are rougher than ME surfaces due to a lar ger prefactor. ME surfaces undergo a ''weakly rough'' to ''algebraical ly rough'' transition in 3d, suggesting a similar behavior in fracture .