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Avalanche and spreading exponents in systems with absorbing states
M A Muñoz1, R Dickman, A Vespignani
1The Abdus Salam International Centre for Theoretical Physics (ICTP), P.O. Box 586, 34100 Trieste, Italy.
Summary
We discovered general scaling laws connecting critical exponents in systems with absorbing states. These laws help understand self-organized criticality and predict nonuniversality in avalanche exponents for complex systems.
Area of Science:
- Statistical Physics
- Complex Systems Theory
Background:
- Systems with absorbing states exhibit critical phenomena.
- Self-organized criticality (SOC) describes systems that naturally evolve to a critical state.
- Understanding the relationship between critical exponents and avalanche behavior is crucial.
Purpose of the Study:
- To establish generic scaling laws relating spreading critical exponents and avalanche exponents.
- To provide updated exponents for key universality classes like directed percolation.
- To clarify the connections between SOC and systems with absorbing states.
Main Methods:
- Derivation of general scaling laws applicable to systems with absorbing states.
- Compilation and presentation of state-of-the-art critical exponents.
- Analysis of avalanche exponents within the framework of the derived scaling laws.
Main Results:
- Generic scaling laws were established, linking critical and avalanche exponents.
- A comprehensive collection of exponents for directed percolation and other universality classes is presented.
- Nonuniversality in avalanche exponents is predicted for systems with multiple absorbing states.
Conclusions:
- The derived scaling laws provide a unified framework for understanding critical phenomena in systems with absorbing states.
- The results offer insights into the nature of self-organized criticality.
- Predictions of nonuniversality highlight the complexity of avalanche behavior in certain systems.