Functional Renormalization Group approach to the Kraichnan model

TL;DR

This paper applies Functional Renormalization Group methods to analyze the anomalous scaling behavior of scalar fields in the Kraichnan model, providing insights into the underlying symmetries and operator dynamics.

Contribution

It introduces a novel application of FRG techniques to the Kraichnan model, focusing on composite operator renormalization and symmetry analysis.

Findings

Identifies leading corrections to structure functions.

Derives anomalous scaling exponents.

Highlights the role of symmetries in the model.

Abstract

We study the anomalous scaling of the structure functions of a scalar field advected by a random Gaussian velocity field, the Kraichnan model, by means of Functional Renormalization Group techniques. We analyze the symmetries of the model and derive the leading correction to the structure functions considering the renormalization of composite operators and applying the operator product expansion.