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Critical exponents for the restricted sandpile.

Ronald Dickman1

  • 1Departamento de Física, ICEx, Universidade Federal de Minas Gerais, Caixa Postal 702, 30161-970 Belo Horizonte, Minas Gerais, Brazil. dickman@fisica.ufmg.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|April 12, 2006
PubMed
Summary

Large-scale simulations of a one-dimensional stochastic sandpile model reveal critical exponents consistent with Langevin equation predictions. This indicates that finite-size effects and scaling corrections explain previous universality discrepancies.

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Area of Science:

  • Complex systems
  • Statistical physics
  • Computational modeling

Background:

  • Stochastic sandpile models are used to study self-organized criticality.
  • Previous studies in one dimension reported deviations from expected universality.
  • The role of finite-size effects and scaling corrections was unclear.

Purpose of the Study:

  • To investigate the critical behavior of a one-dimensional height-restricted stochastic sandpile.
  • To resolve discrepancies in reported critical exponents and universality in 1D sandpiles.
  • To compare simulation results with theoretical predictions from Langevin equations.

Main Methods:

  • Large-scale Monte Carlo simulations were employed.
  • The quasistationary simulation method was utilized for efficiency.

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  • Simulations were performed on systems up to 50,000 sites.

    • Main Results:

    • Estimates for critical exponents were obtained for large systems.
    • Results significantly differed from those of smaller systems.
    • The obtained exponents align with recent Langevin equation predictions for stochastic sandpiles.

    Conclusions:

    • Apparent violations of universality in 1D sandpiles are attributed to strong corrections to scaling.
    • Finite-size effects play a crucial role in observed discrepancies.
    • The study validates theoretical predictions and clarifies universality in this model.