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Classification of universality classes for quasideterministic sandpile models.

Sang Bub Lee1

  • 1Department of Physics, Kyungpook National University, Daegu 41566, Republic of Korea.

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Summary

This study investigates two sandpile models using Monte Carlo simulations. Both models exhibit behaviors consistent with the Manna universality class, challenging previous findings.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Computational Physics

Background:

  • Sandpile models are used to study self-organized criticality.
  • Previous research on specific sandpile models has yielded varying conclusions regarding their universality classes.

Purpose of the Study:

  • To investigate the critical behavior of the two-state rotational sandpile model and a three-state sandpile model.
  • To estimate critical exponents characterizing avalanche properties.
  • To compare simulation results with known universality classes and resolve discrepancies in prior research.

Main Methods:

  • Monte Carlo simulations were employed to model the sandpile dynamics.
  • Probability distributions of avalanche size, area, lifetime, and gyration radius were analyzed.
  • Expectation values of avalanche properties were calculated against time and size-area relationships.

Main Results:

  • Both the two-state rotational and three-state sandpile models yielded consistent results within statistical error.
  • The observed critical exponents and behaviors align with the Manna universality class.
  • The findings contradict earlier conclusions by Santra et al. due to slow convergence issues.

Conclusions:

  • The two-state rotational and three-state sandpile models likely belong to the Manna universality class.
  • Discrepancies with previous studies are attributed to the slow convergence of probability distributions to asymptotic power-law behavior.
  • The study provides a more accurate characterization of these sandpile models' critical phenomena.