In this paper, we compute to high precision the roughness exponent ζ of a long-range elastic string, at the depinning threshold, in a random medium. Our numerical method exploits the analytic structure of the problem (``no-passing'' theorem), but avoids direct simulation of the evolution equations. The roughness exponent has recently been studied by simulations, functional renormalization-group calculations, and by experiments (fracture of solids, liquid meniscus in 4He). Our result ζ=0.388+/-0.002 is significantly larger than what was stated in previous simulations, which were consistent with a one-loop renormalization-group calculation. Furthermore, the data are incompatible with the experimental results for crack propagation in solids and for a 4He contact line on a rough substrate. This implies that the experiments cannot be described by pure harmonic long-range elasticity in the quasistatic limit.
Physical Review E
- Pub Date:
- February 2002
- General studies of phase transitions;
- Wave propagation fracture and crack healing;
- Condensed Matter - Disordered Systems and Neural Networks
- 4 pages, 3 figures