Dynamically Driven Renormalization Group

TL;DR

The paper introduces the Dynamically Driven Renormalization Group (DDRG), a new real-space renormalization method for analyzing non-equilibrium critical steady-states in dynamical systems, enabling analytical evaluation of scaling properties.

Contribution

It develops a novel DDRG scheme driven by a steady-state condition, applicable to non-linear open systems and equilibrium models, providing analytical tools for critical phenomena analysis.

Findings

Applied DDRG to self-organized critical systems.

Enabled analytical calculation of critical exponents.

Demonstrated applicability to equilibrium critical models.

Abstract

We present a detailed discussion of a novel dynamical renormalization group scheme: the Dynamically Driven Renormalization Group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical steady-state. The method is based on a real space renormalization scheme driven by a dynamical steady-state condition which acts as a feedback on the transformation equations. This approach has been applied to open non-linear systems such as self-organized critical phenomena, and it allows the analytical evaluation of scaling dimensions and critical exponents. Equilibrium models at the critical point can also be considered. The explicit application to some models and the corresponding results are discussed.