p}$, and exhibits irregular fluctuations with a standard deviation of the order of $\xi$ while keeping its original orientation on scales above $L_{\rm p}$. This allows us to obtain estimates of the pinning length directly from the shape of the relaxed line.

Averaging the pinning force over the pinning length defines a characteristic force per unit length. If the external force is smaller than this effective pinning force, the line is likely to be trapped into some metastable configuration. If the external force is large enough to make all metastable configurations disappear, the line will move indefinitely (depinning). The critical force for depinning can be estimated by comparing the external force to the pinning force, averaged over the pinning length. This gives $$f_{\rm ext,c}= \hat{f} \sqrt{\frac{\xi}{L_{\rm p}}} = \hat{f}^{4/3} {\cal T}^{-1/3} \xi^{1/3}.
\label{eq:fpin}$$ In the context of dislocation theory, this argument corresponds to the weak pinning limit. An interesting aspect is that, if the pinning length is known, we may relate the critical force directly to the pinning length by eliminating the characteristic force $\hat{f}$ from Eqs. (\[eq:lpin\]) and (\[eq:fpin\]) to obtain $$f_{\rm ext,c}= \frac{{\cal T}\xi^{1/3}}{L_{\rm p}^2}.
\label{eq:fpinL}$$ As we shall demonstrate, this relationship allows to obtain, in the weak 