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Abrupt transition in a sandpile model.

Y F Contoyiannis1, F K Diakonos

  • 1Department of Physics, University of Athens, GR-15771 Athens, Greece. fdiakono@phys.uoa.gr

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

We introduce a novel fixed energy sandpile model that exhibits a discontinuous transition with increasing energy. This new model, based on modified Bak-Tang-Wiesenfeld rules, allows microscopic exploration of abrupt phase transitions.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Self-Organized Criticality

Background:

  • The Bak-Tang-Wiesenfeld (BTW) model is a foundational model for self-organized criticality.
  • Standard BTW models typically exhibit continuous phase transitions.

Purpose of the Study:

  • To present a modified sandpile model exhibiting discontinuous transitions.
  • To investigate the microscopic mechanisms driving abrupt transitions in complex systems.

Main Methods:

  • Modified the toppling procedure of the Bak-Tang-Wiesenfeld (BTW) rules.
  • Introduced a negative gradient constraint for energy transfer.
  • Implemented asynchronous time ordering for toppling events.

Main Results:

  • The modified sandpile model shows a discontinuous transition with increasing initial energy.
  • Removing either the negative gradient or asynchronous constraint results in a continuous transition, similar to the standard BTW model.

Conclusions:

  • The proposed model is minimal, with specific constraints being essential for the discontinuous transition.
  • This model provides a unique platform for studying the fundamental mechanisms of abrupt transitions at a microscopic level.

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