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Related Experiment Videos

Nonequilibrium critical behavior in unidirectionally coupled stochastic processes.

Y Y Goldschmidt1, H Hinrichsen, M Howard

  • 1Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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This study explores multicritical behavior in hierarchical reaction-diffusion systems, revealing reduced density exponents and a new crossover exponent. Simulations confirm the crossover to directed percolation (DP) universality classes in lower dimensions.

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Non-equilibrium Systems

Background:

  • Phase transitions to absorbing states are often described by directed percolation (DP) universality.
  • Single-species reaction-diffusion systems realize DP with specific reaction rules.
  • Hierarchical coupling of DP processes can lead to multicritical behavior.

Purpose of the Study:

  • Investigate multicritical phenomena in unidirectionally coupled reaction-diffusion systems.
  • Determine density exponents and crossover exponents in these hierarchical DP models.
  • Connect theoretical predictions with simulation results and applications.

Main Methods:

  • Field-theoretic renormalization-group techniques in d=4-epsilon dimensions.
  • Mean-field rate equation analysis.

Related Experiment Videos

  • Monte Carlo simulations in dimensions d<=3.

    • Main Results:

    • Identified multicritical behavior with reduced density exponents beta(i)=1/(2(i-1)).
    • Computed a new crossover exponent phi=1+O(epsilon(2)) for the second hierarchy level.
    • Calculated fluctuation corrections to density exponents and confirmed crossover to ordinary DP.

    Conclusions:

    • The hierarchical coupling of DP processes leads to distinct multicritical behavior.
    • Theoretical predictions are validated by Monte Carlo simulations.
    • The findings apply to growth processes, cellular automata, and pair annihilation systems.