Origin of the roughness exponent in elastic strings at the depinning threshold

Alberto Rosso (1) , Werner Krauth (1)

1 LPS - Laboratoire de Physique Statistique de l'ENS

Within a recently developed framework of dynamical Monte Carlo algorithms, we compute the roughness exponent $\zeta$ of driven elastic strings at the depinning threshold in 1+1 dimensions for different functional forms of the (short-range) elastic energy. A purely harmonic elastic energy leads to an unphysical value for $\zeta$. We include supplementary terms in the elastic energy of at least quartic order in the local extension. We then find a roughness exponent of $\zeta \simeq 0.63$, which coincides with the one obtained for different cellular automaton models of directed percolation depinning. The quartic term translates into a nonlinear piece which changes the roughness exponent in the corresponding continuum equation of motion. We discuss the implications of our analysis for higher-dimensional elastic manifolds in disordered media.

Domaines: Autre [cond-mat.other]

Alberto Rosso, Werner Krauth. Origin of the roughness exponent in elastic strings at the depinning threshold. Physical Review Letters, 2001, 87, pp.187002. ⟨hal-00126168⟩