Chauve P, Le Doussal P, Wiese K J
CNRS-Laboratoire de Physique des Solides, Université de Paris-Sud, Orsay, France.
Phys Rev Lett. 2001 Feb 26;86(9):1785-8. doi: 10.1103/PhysRevLett.86.1785.
We study the field theories for pinned elastic systems at equilibrium and at depinning. Their beta functions differ to two loops by novel "anomalous" terms. At equilibrium we find a roughness zeta = 0.208 298 04 epsilon + 0.006 858 epsilon(2) (random bond), zeta = epsilon/3 (random field). At depinning we prove two-loop renormalizability and that random field attracts shorter range disorder. We find zeta = epsilon/3(1 + 0.143 31 epsilon), epsilon = 4 - d, in violation of the conjecture zeta = epsilon/3, solving the discrepancy with simulations. For long range elasticity zeta = epsilon/3(1 + 0.397 35 epsilon), epsilon = 2 - d, much closer to the experimental value (approximately 0.5 both for liquid helium contact line depinning and slow crack fronts) than the standard prediction 1/3.
我们研究了处于平衡态和脱钉态的 pinned 弹性系统的场论。它们的β函数在两圈阶次上因新颖的“反常”项而有所不同。在平衡态，我们发现粗糙度ζ = 0.20829804ε + 0.006858ε²（随机键），ζ = ε/3（随机场）。在脱钉态，我们证明了两圈可重整化性，并且随机场吸引较短程无序。我们发现ζ = ε/3(1 + 0.14331ε)，ε = 4 - d，这与ζ = ε/3的猜想相悖，解决了与模拟结果的差异。对于长程弹性，ζ = ε/3(1 + 0.39735ε)，ε = 2 - d，比标准预测值1/3更接近实验值（液氦接触线脱钉和缓慢裂纹前沿的实验值均约为0.5）。
