Kay Joerg Wiese

Driven particle in a random landscape: disorder correlator, avalanche distribution, and extreme value statistics of records.

We review how the renormalized force correlator Delta(micro) , the function computed in the functional renormalization-group (RG) field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in the presence of pinning disorder. We show how this function can be computed analytically for a particle dragged through a one-dimensional random-force landscape. The limit of small velocity allows one to access the critical behavior at the depinning transition. For uncorrelated forces one finds three universality classes, corresponding to the three extreme value statistics, Gumbel, Weibull, and Fréchet. For each class we obtain analytically the universal function Delta(micro) , the corrections to the critical force, and the joint probability distribution of avalanche sizes s and waiting times w . We find P(s)=P(w) for all three cases. All results are checked numerically. For a Brownian force landscape, known as the Alessandro, Beatrice, Bertotti, and Montorsi (ABBM) model, avalanche distributions and Delta(micro) can be computed for any velocity. For two-dimensional disorder, we perform large-scale numerical simulations to calculate the renormalized force correlator tensor Delta_{ij}(micro[over ]) , and to extract the anisotropic scaling exponents zeta_{x}>zeta_{y} . We also show how the Middleton theorem is violated. Our results are relevant for the record statistics of random sequences with linear trends, as encountered, e.g., in some models of global warming. We give the joint distribution of the time s between two successive records and their difference in value w .

Functional renormalization group at large N for disordered systems.

We introduce a method, based on an exact calculation of the effective action at large N, to bridge the gap between mean-field theory and renormalization in complex systems. We apply it to a d-dimensional manifold in a random potential for large embedding space dimension N. This yields a functional renormalization group equation valid for any d, which contains both the O(epsilon=4-d) results of Balents-Fisher and some of the nontrivial results of the Mezard-Parisi solution, thus shedding light on both. Corrections are computed at order O(1/N). Applications to the Kardar-Parisi-Zhang growth model, random field, and mode coupling in glasses are mentioned.

Avalanche-size distribution at the depinning transition: A numerical test of the theory

We calculate numerically the sizes

On the Perturbation Expansion of the KPZ Equation

S

Universal interface width distributions at the depinning threshold

of jumps (avalanches) between successively pinned configurations of an elastic line

New renormalization group results for scaling of self-avoiding tethered membranes

(d=1)

Height fluctuations of a contact line: A direct measurement of the renormalized disorder correlator

or interface

Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition

(d=2)

Higher correlations, universal distributions, and finite size scaling in the field theory of depinning.

, pulled by a spring of (small) strength

Random-Field Spin Models beyond 1 Loop: A Mechanism for Decreasing the Lower Critical Dimension

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