Two-loop functional renormalization group theory of the depinning transition
Two-loop functional renormalization group theory of the depinning transition
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DOI：
10.1103/physrevb.66.174201
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发表时间：
2002-11-01
影响因子：
3.7
通讯作者：
Chauve, P
中科院分区：
文献类型：
--
作者：
Le Doussal, P;Wiese, KJ;Chauve, P
我们构造了零温度下界面和弹性周期系统的准静态各向同性脱钉场论，适当考虑了动力学作用的非解析形式。这就解决了单回路流动方程不能区分静态和准静态脱钉的问题，从而解释了后者的不可逆性。我们证明了两个循环的重整化，获得两个循环的β函数，并显示产生的“不可逆”的异常条款，导致从非解析的理论，这导致静力学和驱动动力学不同的两个循环。我们给出指数zeta（粗糙度）和z（动力学）的阶数为π（2）。这测试了以前基于单圈结果的假设：它表明随机场无序确实吸引了所有短程无序。猜想zeta= /3是不正确的，违反zeta=（/3）（1+ 0.14331），=4-d。这解决了长期以来与模拟的差异。对于长期弹性zeta=（λ/3）（1+ 0.39735 λ），λ =2-d（与d=1的标准预测zeta=1/3相比），与模拟结果合理一致。讨论了氦接触线脱钉和慢裂纹前沿实验中zeta值接近0.5的情况。
We construct the field theory of quasistatic isotropic depinning for interfaces and elastic periodic systems at zero temperature, taking properly into account the nonanalytic form of the dynamical action. This cures the inability of the one-loop flow equations to distinguish between statics and quasistatic depinning, and thus to account for the irreversibility of the latter. We prove two-loop renormalizability, obtain the two-loop beta-function and show the generation of "irreversible" anomalous terms, resulting from the nonanalyticity of the theory, which cause statics and driven dynamics to differ at two loops. We give the exponents zeta (roughness) and z (dynamics) to order epsilon(2). This tests previous conjectures based on the one-loop result: It shows that random-field disorder indeed attracts all shorter range disorder. The conjecture zeta=epsilon/3 is incorrect, with violation zeta=(epsilon/3)(1+0.14331epsilon), epsilon=4-d. This solves a longstanding discrepancy with simulations. For long-range elasticity zeta=(epsilon/3)(1+0.39735epsilon), epsilon=2-d (vs the standard prediction zeta=1/3 for d=1), in reasonable agreement with simulations. The high value of zetaapproximate to0.5 in experiments both on Helium contact line depinning and on slow crack fronts is discussed.