Disordered elastic systems and one-dimensional interfaces
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...At larger scales, disorder plays a key role inducing a different power law-scaling ∼ r [30, 47, 48]....
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Cites background from "Disordered elastic systems and one-..."
...Therefore, a statistical approach is necessary to incorporate the effects of randomness in a real sample, and is given by the general model of a fluctuating elastic manifold in a disordered medium [19, 87]....
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References
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139,059 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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...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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1,015 citations