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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

|August 16, 2013

Summary

This summary is machine-generated.

Stiff directed lines in 1+d dimensions localize with increasing disorder for d>2/3. This study reveals a novel relation between stiff directed line localization and directed lines under tension, impacting critical behavior analysis.

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Area of Science:

Condensed Matter Physics
Statistical Mechanics
Disordered Systems

Background:

Directed lines with bending energy are fundamental in various physical systems.
Understanding their behavior under random potentials is crucial for materials science and statistical physics.

Purpose of the Study:

To investigate the localization transition of stiff directed lines in a random potential.
To establish a relationship between the localization of stiff directed lines and directed lines under tension.
To analyze the properties of the disorder-dominated phase.

Main Methods:

Perturbative arguments
Flory scaling arguments
Variational replica calculation
Functional renormalization
Numerical transfer matrix calculations
Multifractal analysis

Main Results:

A localization transition occurs for stiff directed lines in 1+d dimensions when d>2/3 with increasing disorder.
A novel relation is proposed between stiff directed line localization and directed lines under tension, supported by identical free-energy distributions.
The persistence length of stiff directed lines is quantified to be reduced by disorder.

Conclusions:

Pair interactions in the replicated Hamiltonian are key to directed line localization transitions.
The findings have implications for the critical behavior of the Kardar-Parisi-Zhang equation.
An Anderson transition-like scenario and matching correlation length exponent are observed.