# Disordered elastic systems and one-dimensional interfaces

Abstract: We briefly introduce the generic framework of disordered elastic systems (DES), giving a short ‘recipe’ of a DES modeling and presenting the quantities of interest in order to probe the static and dynamical disorder-induced properties of such systems. We then focus on a particular low-dimensional DES, namely the one-dimensional interface in short-ranged elasticity and short-ranged quenched disorder. Illustrating different elements given in the introductory sections, we discuss specifically the consequences of the interplay between a finite temperature T > 0 and a finite interface width ξ > 0 on the static geometrical fluctuations at different lengthscales, and the implications on the quasistatic dynamics.

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### Cites background from "Disordered elastic systems and one-..."

...(a) Interface velocity v as a function of the driving force F , adapted from [29]....

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...In the case of more general disorder, it may also be necessary to consider all the n-th order moments of the probability distribution function (PDF) of relative displacements ∆u(r), which reflect the characteristic scaling properties of the system [29]:...

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...(d) The roughness B(r) of the interface grows with the length scale r, adapted from [29]....

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...(a) Relative displacement ∆u(r) for r = z2 − z1 of a one-dimensional interface from its flat, elastically optimal configuration under the influence of weak collective pinning in a disorder potential, adapted from [29] (b) Random bond disorder preserves the symmetry of the double-well potential, while locally changing its depth....

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##### References

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123,310 citations

### "Disordered elastic systems and one-..." refers background in this paper

...the imaging of the imbibition line of a fluid on a disordered substrate [26], of a crack front along an heterogeneous weak plane [27] by ultra-fast CCD camera, or of avalanches in ferromagnetic thin films [5]....

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### "Disordered elastic systems and one-..." refers methods in this paper

...We first used the so-called ‘replica trick’, well-known in the study of spin glasses [39], in order to average first over the disorder and so to transform the random part Hdis in the full Hamiltonian of one interface (u1), into an effective non-random coupling between n copies of the interface (u1⁄4 fu1, ....

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...The two main analytical tools used on DES are on one hand the Functional Renormalization Group (FRG) where the whole disorder correlator (3) evolves under the renormalization procedure [17,34–37], and on the other hand the Gaussian Variational Method (GVM) as introduced by Mézard and Parisi on DES, and involving Replica to treat the disorder [38,39]....

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1,308 citations

### "Disordered elastic systems and one-..." refers background in this paper

...ferroelectric [1, 2, 3] or ferromagnetic [4, 5, 6] domain walls, contact line in wetting experiments [7] or propagating cracks in paper and thin materials [8]) or periodic systems (typically vortex lattices in type-II superconductors [9], classical [10] or quantum [11] Wigner crystals, or electronic crystals displaying charge or spin density waves [12, 13])....

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956 citations