Large scale numerical simulations of "ultrametric" long-range depinning

Details Large scale numerical simulations of "ultrametric" long-range depinning Large scale numerical simulations of "ultrametric" long-range depinning

2004-01-26

arxiv.org/abs/cond-mat/0401522v1

Physical Review E 70 (2004) 026103

Physics

Condensed Matter

Other Condensed Matter

submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.70.026103

The depinning of an elastic line interacting with a quenched disorder is studied for long range interactions, applicable to crack propagation or wetting. An ultrametric distance is introduced instead of the Euclidean distance, allowing for a drastic reduction of the numerical complexity of the problem. Based on large scale simulations, two to three orders of magnitude larger than previously considered, we obtain a very precise determination of critical exponents which are shown to be indistinguishable from their Euclidean metric counterparts. Moreover the scaling functions are shown to be unchanged. The choice of an ultrametric distance thus does not affect the universality class of the depinning transition and opens the way to an analytic real space renormalization group approach.

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