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Functional renormalization group approach to the Kraichnan model.
1Institut für Physik (WA THEP), Johannes-Gutenberg-Universität, Staudingerweg 7, 55099 Mainz, Germany.
We investigated anomalous scaling in the Kraichnan model using functional renormalization group methods. Our analysis reveals leading corrections to structure functions by considering operator renormalization and expansion.
Area of Science:
- * Physics
- * Statistical Mechanics
- * Fluid Dynamics
Background:
- * The Kraichnan model describes a scalar field advected by a random Gaussian velocity field.
- * Understanding anomalous scaling in such systems is crucial for various physical phenomena.
Purpose of the Study:
- * To investigate the anomalous scaling of structure functions in the Kraichnan model.
- * To derive the leading corrections to these structure functions.
Main Methods:
- * Employed functional renormalization group techniques.
- * Analyzed the symmetries inherent to the model.
- * Utilized operator product expansion and considered renormalization of composite operators.
Main Results:
- * Derived the leading correction terms for the structure functions.
- * Demonstrated the application of functional renormalization group to this complex system.
Conclusions:
- * The study provides a detailed analysis of anomalous scaling in the Kraichnan model.
- * The methods used offer a pathway to study similar complex systems in statistical physics.
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