Localization transition of stiff directed lines in random media.
We investigate the localization of stiff directed lines with bending energy by a short-range random potential. Using perturbative arguments, Flory arguments, and a replica calculation, 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.
Physics Department, TU Dortmund University, 44221 Dortmund, Germany. horst-holger.boltz@udo.edu
Horst-Holger
HH
Boltz
Jan
J
Kierfeld
D000199:Actins / Q000737:chemistry; D001703:Biophysics / Q000379:methods*; D003599:Cytoskeleton / Q000737:chemistry; D004247:DNA / Q000737:chemistry; D004548:Elasticity; D007700:Kinetics; D008962:Models, Theoretical; D016011:Normal Distribution; D011108:Polymers / Q000737:chemistry; D013269:Stochastic Processes; D013696:Temperature; D013816:Thermodynamics
D000199:Actins; D011108:Polymers; D004247:DNA