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Logarithmic corrections in dynamic isotropic 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
|October 4, 2003
PubMed
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This study explores logarithmic corrections in dynamic percolation at d=6 using field theory and renormalization group methods. We calculated key observables like active sites and survival probability for seeded clusters.

Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Dynamic isotropic percolation models critical phenomena.
  • Understanding scaling corrections is crucial for precise predictions.

Purpose of the Study:

  • Investigate logarithmic corrections to scaling in dynamic percolation.
  • Determine these corrections at the upper critical dimension (d=6).
  • Analyze time-dependent observables at the critical point.

Main Methods:

  • Field theoretic formulation of the general epidemic process.
  • Renormalization group (RG) methods.
  • Calculation of next-to-leading order corrections.

Main Results:

  • Logarithmic corrections to scaling were determined for dynamic percolation at d=6.

Related Experiment Videos

  • Calculated corrections for the number of active sites, radius of gyration, and survival probability.
  • Analysis focused on clusters seeded from a local origin.

    • Conclusions:

    • The study provides precise corrections to scaling for dynamic percolation observables.
    • Findings enhance theoretical understanding of critical phenomena in disordered systems.
    • Results are applicable to systems exhibiting epidemic-like spreading dynamics.