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Functional renormalization group at large N for disordered systems.
Pierre Le Doussal1, Kay Jörg Wiese
1CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris, France.
Physical Review Letters
|September 13, 2002
Summary
We present a new method for analyzing complex systems by exactly calculating effective actions. This approach bridges mean-field theory and renormalization, offering insights into diverse physical models.
Area of Science:
- Statistical Physics
- Condensed Matter Physics
- Theoretical Physics
Background:
- Bridging the gap between mean-field theory and renormalization is crucial for understanding complex systems.
- Existing methods often struggle to capture the full complexity of these systems.
- Large N expansions provide a powerful tool for analytical approximations.
Purpose of the Study:
- To introduce a novel method for analyzing complex systems by calculating effective actions.
- To develop a functional renormalization group equation applicable to various dimensions.
- To reconcile and illuminate results from existing theories like Balents-Fisher and Mezard-Parisi.
Main Methods:
- Exact calculation of the effective action at large N (number of dimensions).
- Application to a d-dimensional manifold in a random potential.
- Derivation of a functional renormalization group equation.
Main Results:
- A functional renormalization group equation valid for any dimension d is derived.
- The equation incorporates elements from both O(epsilon=4-d) and Mezard-Parisi solutions.
- Corrections at order O(1/N) are computed, providing refined analytical insights.
Conclusions:
- The developed method offers a unified framework for studying complex systems.
- It provides a deeper understanding of the relationship between different theoretical approaches.
- Potential applications span diverse areas including growth models, random fields, and glassy dynamics.