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

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

2006-10-30

arxiv.org/abs/cond-mat/0610821v1

Phys. Rev. B 75 (2007) 220201

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 6 figures

Scientific paper

10.1103/PhysRevB.75.220201

We compute numerically the sequence of successive pinned configurations of an elastic line pulled quasi-statically by a spring in a random bond (RB) and random field (RF) potential. Measuring the fluctuations of the center of mass of the line allows to obtain the functional renormalization group (FRG) functions at the depinning transition. The universal form of the second cumulant Delta(u) is found to have a linear cusp at the origin, to be identical for RB and RF, different from the statics, and in good agreement with 2-loop FRG. The cusp is due to avalanches, which we visualize. Avalanches also produce a cusp in the third cumulant, whose universal form is obtained, as predicted by FRG.

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