David C. Kaspar, Muhittin Mungan
We present a simplified charge density wave (CDW) model exhibiting a depinning transition with threshold force and configurations that are explicit. Due to the periodic boundary conditions imposed, the threshold configuration has a set of topological defects whose location and number depend on the realization of the random phases. These defects are responsible for the randomness of the threshold force, which, as the system size $L \to \infty$, approaches a Gaussian with variance scaling as $L^{-1}$. The approach to threshold proceeds via avalanches whose size dependence on the external driving force $F$ is described by a record-breaking process. We find that the depinning transition in this model is a critical phenomenon, with the cumulative avalanche size (polarization) diverging near threshold as $(F_{\rm th} - F)^{-2}$.
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http://arxiv.org/abs/1304.2845
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