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Dynamical scaling behavior of the one-dimensional conserved directed-percolation universality class
1Department of Physics and Research Institute for Basic Sciences, Kyung Hee University, Seoul 130-701, Korea.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study examines dynamical scaling in epidemic and sandpile models. Researchers found consistent dynamical exponents, resolving previous discrepancies in nonequilibrium phase transition research.
Area of Science:
- Statistical Physics
- Complex Systems
- Nonlinear Dynamics
Background:
- Nonequilibrium absorbing phase transitions are critical phenomena observed in various systems.
- The conserved directed-percolation (CDP) or Manna universality class describes systems with conserved quantities and absorbing states.
- Previous studies reported inconsistent dynamical exponents for models within this class, hindering a unified understanding.
Purpose of the Study:
- To investigate the dynamical scaling behavior of the static diffusive epidemic process and a fixed-energy Manna sandpile model.
- To determine consistent dynamical exponents for these models in one dimension.
- To resolve discrepancies arising from finite-size scaling analyses in previous research.
Main Methods:
- Utilized critical spreading simulations of localized activity in absorbing configurations.
- Employed one-dimensional models to study the conserved directed-percolation or Manna universality class.
- Ensured results are free from finite-size effects by avoiding boundary interactions during simulations.
Main Results:
- Obtained consistent estimates of the dynamical exponents for both the epidemic and Manna sandpile models.
- Demonstrated that critical spreading simulations provide reliable data for dynamical exponent determination.
- Resolved the scattered results previously obtained from finite-size scaling analyses.
Conclusions:
- The static diffusive epidemic process and Manna sandpile model exhibit consistent dynamical scaling behavior.
- Critical spreading simulations are effective for accurately measuring dynamical exponents in these systems.
- This work provides a unified understanding of dynamical exponents within the Manna universality class.
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