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Universality class of one-dimensional directed sandpile models
Matthew Stapleton1, Kim Christensen
1Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom. ms599@imperial.ac.uk
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
Summary
A new general n-state directed sandpile model was developed. This model exhibits universal behavior similar to the asymmetric Oslo model, revealing a broad class of one-dimensional sandpile models.
Area of Science:
- Statistical Physics
- Complex Systems
Background:
- Directed sandpile models are used to study self-organized criticality.
- Understanding universality classes is key to classifying complex system behaviors.
Purpose of the Study:
- Introduce a generalized n-state directed sandpile model.
- Analyze its stationary properties and universality class.
Main Methods:
- Derivation of stationary properties for the n-state model.
- Application of analytical arguments using a central limit theorem.
Main Results:
- The n-state model belongs to the universality class of the totally asymmetric Oslo model.
- A crossover to uncorrelated branching process behavior is observed for small system sizes.
Conclusions:
- The central limit theorem identifies a large universality class for one-dimensional directed sandpile models.
- This generalized model provides a framework for studying diverse self-organized critical phenomena.