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DY: Fachverband Dynamik und Statistische Physik

DY 56: Poster - Statistical Physics

DY 56.11: Poster

Thursday, March 19, 2015, 16:00–18:00, Poster A

Stiff Directed Lines in Random Media — •Horst-Holger Boltz and Jan Kierfeld — TU Dortmund, Dortmund, Germany

We investigate the behaviour of stiff directed lines with bending energy in a random medium. We show that a stiff directed line in 1+d dimensions undergoes a localization transition with increasing disorder for d>2/3. We demonstrate that this transition is accessible by numerical transfer matrix calculations in 1+1 dimensions and analyze the properties of the disorder-dominated phase. On the basis of the two-replica problem, we propose a relation between the localization of stiff directed lines in 1+d dimensions and of directed lines under tension in 1+3d dimensions, which is strongly supported by identical free energy distributions. This shows that pair interactions in the replicated Hamiltonian determine the nature of directed line localization transitions with consequences for the critical behavior of the Kardar-Parisi-Zhang (KPZ) equation. Furthermore, we quantify how the persistence length of the stiff directed line is reduced by disorder. Additionally, we study the depinning of stiff directed lines. Their equation of motion is the (quenched) Herring-Mullins equation, which also describes surface growth governed by surface diffusion. We employ analytical arguments and numerical simulations to determine the critical exponents and compare our findings with previous works and functional renormalization group results, which we extend to the different line elasticity. We see evidence for two distinct correlation length exponents.