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Two-loop functional renormalization for elastic manifolds pinned by disorder in N dimensions
Pierre Le Doussal1, Kay Jörg Wiese
1CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75005 Paris, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
Summary
Researchers studied elastic manifolds in random potentials using a functional renormalization group. They determined the fixed point and roughness exponent, offering insights into the Kardar-Parisi-Zhang growth equation and suggesting an upper critical dimension.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Field Theory
Background:
- Elastic manifolds in random potentials are crucial for understanding disordered systems.
- Previous work established a renormalizable field theory for N=1.
- Extending this framework to N>1 is essential for broader applicability.
Purpose of the Study:
- To investigate elastic manifolds in N-dimensional random potentials.
- To extend a two-loop renormalizable field theory to N>1.
- To determine the fixed point and roughness exponent for isotropic disorder with O(N) symmetry.
Main Methods:
- Functional Renormalization Group (FRG) approach.
- Development of a field theory renormalizable to two loops for N>1.
- Analysis of the epsilon expansion (epsilon=4-d) for the internal dimension 'd'.
Main Results:
- Obtained the fixed point and roughness exponent to next-to-leading order in epsilon.
- Extrapolated results to the directed polymer limit (d=1).
- Provided insights into the strong coupling phase of the N-dimensional Kardar-Parisi-Zhang (KPZ) equation.
Conclusions:
- The study suggests an upper critical dimension d(u) approximately 2.5 for these systems.
- The findings offer a handle on the strong coupling regime of the KPZ equation.
- The extended field theory provides a powerful tool for studying disordered elastic systems.