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Published on: May 20, 2014
Static fluctuations of a thick one-dimensional interface in the 1+1 directed polymer formulation
Elisabeth Agoritsas1, Vivien Lecomte, Thierry Giamarchi
1DPMC-MaNEP, University of Geneva, 24 Quai Ernest-Ansermet, 1211 Geneva 4, Switzerland. elisabeth.agoritsas@unige.ch
Summary
This study analyzes one-dimensional interfaces using directed polymers, revealing how finite width and quenched disorder affect fluctuations. A new toy model simplifies understanding interface behavior across temperatures and disorder correlations.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Disordered Systems
Background:
- One-dimensional interfaces have a finite width, crucial below a characteristic temperature.
- Thermal fluctuations and microscopic width influence interface behavior.
- Directed polymers provide an exact mapping for static 1D interfaces.
Purpose of the Study:
- To analytically study free-energy and geometrical fluctuations of directed polymers.
- To investigate the impact of quenched random-bond Gaussian disorder with finite correlation length.
- To develop a simplified model for interface properties.
Main Methods:
- Exact mapping of 1D interfaces to 1+1 directed polymers.
- Derivation of exact time-evolution equations for disorder free energy and correlators.
- Linearized evolution solution and construction of a 'toy model' based on asymptotic properties.
Main Results:
- Derived exact evolution equations for disorder free energy and its correlators.
- Developed a 'toy model' with Gaussian Brownian-type free-energy fluctuations.
- Predicted temperature and disorder correlation length dependencies for fluctuation amplitude (D̃(∞)).
Conclusions:
- The toy model provides a simple description of directed polymer properties.
- Identified connections between temperature-induced crossovers and replica symmetry breaking.
- Discussed implications for experimental Kardar-Parisi-Zhang interfaces like magnetic domain walls and liquid crystals.
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