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Driven elastic manifolds in random media exhibit a depinning transition to astate with non-vanishing velocity at a critical driving force. We study thedepinning of stiff directed lines, which are governed by a bending rigidityrather than line tension. Their equation of motion is the (quenched)Herring-Mullins equation, which also describes surface growth governed bysurface diffusion. Stiff directed lines are particularly interesting as thereis a localization transition in the static problem at a finite temperature andthe commonly exploited time ordering of states by means of Middleton's theorems(A. Middleton, Phys. Rev. Lett. 68, 670 (1992)) is not applicable. We employanalytical arguments and numerical simulations to determine the criticalexponents and compare our findings with previous works and functionalrenormalization group results, which we extend to the different lineelasticity. We see evidence for two distinct correlation length exponents.

Depinning of stiff directed lines in random media