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Critical behavior and Griffiths effects in the disordered contact process.

Thomas Vojta1, Mark Dickison

  • 1Department of Physics, University of Missouri-Rolla, Rolla, Missouri 65409, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
Summary

This study investigates nonequilibrium phase transitions in disordered systems using large-scale simulations. Findings reveal activated dynamical scaling at critical points, indicating universal behavior even with weak disorder.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Disordered Systems

Background:

  • The behavior of systems with quenched disorder is crucial for understanding complex phenomena.
  • Nonequilibrium phase transitions present unique challenges compared to equilibrium transitions.
  • Previous predictions suggested an infinite-randomness fixed point for such systems.

Purpose of the Study:

  • To investigate the nonequilibrium phase transition in a one-dimensional contact process with quenched spatial disorder.
  • To verify predictions of an infinite-randomness fixed point.
  • To characterize the dynamical scaling and critical behavior in the presence of disorder.

Main Methods:

  • Large-scale Monte Carlo simulations were employed.
  • Simulations covered extensive time scales (up to 10^9) and system sizes (up to 10^7 sites).

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  • Analysis focused on dynamical scaling and critical exponents.

    • Main Results:

    • Simulations demonstrate activated (exponential) dynamical scaling at the critical point, consistent with an infinite-randomness fixed point.
    • Critical behavior is universal, even for weak disorder.
    • A slow crossover to asymptotic behavior was observed, with crossover times exceeding 10^4.
    • In the Griffiths region, power-law dynamical behavior with continuously varying exponents was found.

    Conclusions:

    • The study confirms activated dynamical scaling and universality in the one-dimensional contact process with quenched disorder.
    • Rare region effects significantly influence phase transitions in disordered systems.
    • Findings have broader implications for theories of phase transitions with quenched disorder.