Rosso Alberto, Krauth Werner
CNRS-Laboratoire de Physique Statistique, Ecole Normale Supérieure, 24, rue Lhomond, 75231 Paris Cedex 05, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Feb;65(2 Pt 2):025101. doi: 10.1103/PhysRevE.65.025101. Epub 2002 Jan 23.
In this paper, we compute to high precision the roughness exponent zeta 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 zeta=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.
在本文中，我们高精度地计算了在随机介质中，处于脱钉阈值的长程弹性弦的粗糙度指数ζ。我们的数值方法利用了该问题的解析结构（“不通过”定理），但避免了对演化方程的直接模拟。粗糙度指数最近已通过模拟、泛函重整化群计算以及实验（固体断裂、4He中的液体弯月面）进行了研究。我们得到的结果ζ = 0.388 ± 0.002，显著大于先前模拟中所给出的结果，那些模拟结果与单圈重整化群计算结果一致。此外，这些数据与固体中裂纹扩展以及粗糙基底上4He接触线的实验结果不相符。这意味着在准静态极限下，实验不能用纯谐波长程弹性来描述。
