adjust their line shape to minimize their energy in the random pinning field. The corresponding structure factor is shown in Figure \[fig:pinlength\]: On small scales one finds an increasing $R(d)$ function with an approximately linear dependency, $R \propto d^{\zeta}$ with $\zeta =1$, as indicative for an inclined dislocation line that has moved under the influence of random forces while remaining locally straight. On large scales the function $R(d)$ is constant as indicative of uncorrelated random displacements of the initially straight line in both directions. A crossover length $L_{\rm p}$ can be constructed as shown in Figure \[fig:pinlength\] by fitting two curves $R \propto d$ and $R = {\rm const.}$ to the two branches and identifying the crossover length (’pinning length’) with the intersection point.

Results are shown in Figure \[fig:pinlength\], top which shows the thus determined pinning length as a function of the strength of the pinning field. As expected according to , the pinning length decreases with increasing pinning field. However, this decrease is only in the regime of weak pinning fields quantitatively described by the theoretical slope of -2/3. At large fields, the pinning length saturates because $L_{\rm p}$ cannot become larger than the physical spacing $\xi$ of 