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Logarithmic corrections in directed percolation.

Hans-Karl Janssen1, Olaf Stenull

  • 1Institut für Theoretische Physik III, Heinrich-Heine-Universität 40225, Düsseldorf, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 5, 2004
PubMed
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We analyzed directed percolation at d=4, finding logarithmic corrections to mean-field behavior. Our study quantifies these corrections for cluster properties and the equation of state.

Area of Science:

  • Statistical Physics
  • Complex Systems
  • Dynamical Systems

Background:

  • Directed percolation is a fundamental model for phase transitions in systems with quenched disorder and continuous symmetry.
  • At the upper critical dimension (d=4), mean-field theory breaks down due to strong critical fluctuations.
  • Understanding these fluctuations is crucial for accurately describing system behavior.

Purpose of the Study:

  • To investigate directed percolation at the upper critical dimension (d=4).
  • To determine logarithmic corrections to critical phenomena.
  • To analyze cluster properties (mass, radius of gyration, survival probability) and the equation of state.

Main Methods:

  • Renormalized dynamical field theory was employed.
  • Analysis focused on critical fluctuations and their impact on system observables.

Related Experiment Videos

  • Calculations included leading and next-to-leading order logarithmic corrections.

    • Main Results:

    • Logarithmic corrections to the mass, radius of gyration, and survival probability of directed percolation clusters were determined.
    • The leading and next-to-leading order logarithmic corrections were explicitly calculated.
    • Logarithmic corrections to the equation of state for stationary particle density were derived.

    Conclusions:

    • Critical fluctuations significantly modify mean-field predictions at d=4.
    • The derived logarithmic corrections provide a more accurate description of directed percolation at its upper critical dimension.
    • This work advances the understanding of critical phenomena in complex systems.