We compare the roughness of minimal energy (ME) surfaces and scalar “quasistatic” fracture (SQF) surfaces. Two-dimensional ME and SQF surfaces have the same roughness scaling, ( is the system size) with . The 3d ME and SQF results at strong disorder are consistent with the random-bond Ising exponent ( is the bulk dimension). However, 3d SQF surfaces are rougher than ME surfaces due to a larger prefactor. ME surfaces undergo a “weakly rough” to “algebraically rough” transition in 3d, suggesting a similar behavior in fracture.
- Received 24 July 1997
- Published in the issue dated 12 January 1998
© 1998 The American Physical Society