Universal interface width distributions at the depinning threshold

Abstract

We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well approximated by a generalized Gaussian theory of independant modes which decay with a characteristic propagator G(q)=1/q^(d+2 zeta); zeta, the roughness exponent, is computed independently. A functional renormalization analysis explains this result and allows to compute the small deviations, i.e. a universal kurtosis ratio, in agreement with numerics. We stress the importance of the Gaussian theory to interpret numerical data and experiments.

4 pages revtex4. See also the following article cond-mat/0301465

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• First-principle derivation of static avalanche-size distribution
• Perturbation Theory for Fractional Brownian Motion in Presence of Absorbing Boundaries
• Global fluctuations in physical systems: a subtle interplay between sum and extreme value statistics
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• Elastic systems with correlated disorder: Response to tilt and application to surface growth
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• Derivation of the Functional Renormalization Group Beta-Function at order 1/N for Manifolds Pinned by Disorder
• Finite-size effects in roughness distribution scaling
• Maximum relative height of elastic interfaces in random media
• Aging dynamics of non-linear elastic interfaces: the Kardar-Parisi-Zhang equation
• Geometry of Gaussian signals
• Large scale numerical simulations of "ultrametric" long-range depinning
• Universal width distributions in non-Markovian Gaussian processes
• Supersymmetry Breaking in Disordered Systems and Relation to Functional Renormalization and Replica-Symmetry Breaking
• Dimensional crossover and universal roughness distributions in Barkhausen noise
• Universal energy distribution for interfaces in a random field environment
• Origin of the approximate universality of distributions in equilibrium correlated systems
• Scaling of local roughness distributions
• Anisotropic finite-size scaling of an elastic string at the depinning threshold in a random-periodic medium
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• Asymmetric Roughness of Elastic Interfaces at the Depinning Threshold
• Long-range interactions in the avalanches of elastic interfaces
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• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles
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