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Localization transition of stiff directed lines in random media
Horst-Holger Boltz1, Jan Kierfeld
1Physics Department, TU Dortmund University, 44221 Dortmund, Germany. horst-holger.boltz@udo.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 2, 2013
Summary
Stiff directed lines in 1+d dimensions localize with increasing disorder for d>2/3. Disorder reduces the line
Area of Science:
- Statistical mechanics
- Condensed matter physics
- Disordered systems
Background:
- Directed lines with bending energy are fundamental in various physical systems.
- Understanding their behavior under random potentials is crucial for predicting material properties.
Purpose of the Study:
- To investigate the localization transition of stiff directed lines in a random potential.
- To analyze the impact of disorder on line properties and explore connections to other physical phenomena.
Main Methods:
- Perturbative arguments
- Flory arguments
- Replica calculations
- Numerical transfer matrix calculations in 1+1 dimensions
Main Results:
- A localization transition occurs for stiff directed lines in 1+d dimensions when d>2/3 with increasing disorder.
- The transition is numerically accessible in 1+1 dimensions, revealing properties of the disorder-dominated phase.
- A relation is proposed between the localization of stiff directed lines and tensioned directed lines, supported by identical free energy distributions.
Conclusions:
- Pair interactions in the replicated Hamiltonian govern directed line localization transitions.
- These findings have implications for the critical behavior of the Kardar-Parisi-Zhang (KPZ) equation.
- Disorder significantly reduces the persistence length of stiff directed lines.
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