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Dynamical real space renormalization group applied to sandpile models
E V Ivashkevich1, A M Povolotsky, A Vespignani
1Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna 141980, Russia.
Summary
This study introduces a general framework for analyzing self-organized critical sandpile models using a dynamically driven renormalization group. It details the branching nature of sandpile avalanches and their critical behavior.
Area of Science:
- Complex Systems
- Statistical Physics
- Dynamical Systems
Background:
- Self-organized criticality (SOC) describes systems that naturally evolve to a critical state.
- Sandpile models are canonical examples used to study SOC phenomena.
- Standard renormalization group methods require adaptation for nonequilibrium dynamical systems.
Purpose of the Study:
- To formulate a general framework for renormalization group analysis of self-organized critical sandpile models.
- To describe the boundary and bulk critical behavior of these models.
- To provide a detailed description of sandpile avalanche branching.
Main Methods:
- Development of a dynamically driven renormalization group.
- Incorporation of feedback relations from stationarity conditions.
- Application of generating functions from branching processes.
Main Results:
- A general framework for renormalization group analysis of sandpile models is established.
- The boundary and bulk critical behavior of sandpile models are described.
- The branching nature of sandpile avalanches is characterized using generating functions.
Conclusions:
- The dynamically driven renormalization group provides a suitable method for analyzing critical phenomena in sandpile models.
- Understanding avalanche branching is key to characterizing the critical behavior of these complex systems.