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Absorbing-state phase transitions with extremal dynamics.

Ronald Dickman1, Guilherme J M Garcia

  • 1Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Caixa Postal 702, CEP 30123-970, Belo Horizonte-Minas Gerais, Brazil. dickman@fisica.ufmg.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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Extremal dynamics offers a new path to self-organized criticality by tuning order parameters to zero. This study defines extremal absorbing processes and reveals a new universality class for phase transitions.

Area of Science:

  • Complex systems
  • Statistical physics
  • Phase transitions

Background:

  • Extremal dynamics offers a novel approach to self-organized criticality.
  • This framework involves tuning an order parameter to zero, linked to phase transitions into an absorbing state.

Purpose of the Study:

  • To define and study extremal absorbing processes and their connection to extremal dynamics.
  • To investigate critical exponents not accessible through standard methods.
  • To establish a new universality class for absorbing-state phase transitions.

Main Methods:

  • Definition of extremal absorbing processes.
  • Analysis of the Bak-Sneppen (BS) model and its absorbing version.
  • Study of an extremal contact process using mean-field theory and simulations.

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Main Results:

  • Refined estimates for critical exponents in the one-dimensional absorbing BS model.
  • Identification of an "extremal directed percolation" universality class.
  • Demonstration that asymmetric updating is a relevant perturbation for this new class.

Conclusions:

  • Extremal dynamics provides a unique pathway to understanding self-organized criticality and absorbing-state phase transitions.
  • The extremal condition significantly alters critical behavior, leading to new universality classes.
  • This research offers new insights into critical exponents and universality classes in complex systems.