Depinning of elastic manifolds

Details Depinning of elastic manifolds Depinning of elastic manifolds

2002-07-11

arxiv.org/abs/cond-mat/0207288v1

Phys. Rev. E 67, 021602 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.67.021602

We compute roughness exponents of elastic d-dimensional manifolds in (d+1)-dimensional embedding spaces at the depinning transition for d=1,...,4. Our numerical method is rigorously based on a Hamiltonian formulation; it allows to determine the critical manifold in finite samples for an arbitrary convex elastic energy. For a harmonic elastic energy, we find values of the roughness exponent between the one-loop and the two-loop functional renormalization group result, in good agreement with earlier cellular automata simulations. We find that the harmonic model is unstable with respect both to slight stiffening and to weakening of the elastic potential. Anharmonic corrections to the elastic energy allow us to obtain the critical exponents of the quenched KPZ class.

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