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

Damien Vandembroucq (1) , Stéphane Roux (1)

1 SVI - Surface du Verre et Interfaces

The depinning of an elastic line interacting with a quenched disorderis studied for long range interactions, applicable to crackpropagation or wetting. An ultrametric distance is introduced insteadof the Euclidean distance, allowing for a drastic reduction of thenumerical complexity of the problem. Based on large scale simulations,two to three orders of magnitude larger than previously considered, weobtain a very precise determination of critical exponents which areshown to be indistinguishable from their Euclidean metriccounterparts. Moreover the scaling functions are shown to beunchanged. The choice of an ultrametric distance thus does not affectthe universality class of the depinning transition and opens the wayto an analytic real space renormalization group approach.

Domaines: Autre [cond-mat.other]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

Damien Vandembroucq, Stéphane Roux. Large scale numerical simulations of "ultrametric" long-range depinning. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2004, 70, pp.026103. ⟨hal-00001070⟩