Dynamically Driven Renormalization Group

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.

Revised version, 50 LaTex pages, 6 postscript figures

References in corpus (4)

• Scaling laws and simulation results for the self--organized critical forest--fire model
• Exact Results for the One-Dimensional Self-Organized Critical Forest-Fire Model
• Renormalization group approach to the critical behavior of the forest fire model
• Critical Behavior of the Sandpile Model as a Self-Organized Branching Process

Cited by in corpus (9)

• How self-organized criticality works: A unified mean-field picture
• Self-organized criticality as an absorbing-state phase transition
• Dynamically Driven Renormalization Group Applied to Sandpile Models
• Solvable Kinetic Gaussian Model in External Field
• Abrupt transition in a sandpile model
• Exact solution of diffusion limited aggregation in a narrow cylindrical geometry
• Application of a renormalization group algorithm to nonequilibrium cellular automata with one absorbing state
• Novel Position-Space Renormalization Group for Bond Directed Percolation in Two Dimensions
• Local Rigidity in Sandpile Models