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Multifractality of self-avoiding walks on percolation clusters.

Viktoria Blavatska1, Wolfhard Janke

  • 1Institut für Theoretische Physik and Centre for Theoretical Sciences (NTZ), Universität Leipzig, Postfach 100 920, Leipzig, Germany. viktoria@icmp.lviv.ua

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This study explores self-avoiding walks on percolation clusters using numerical simulations. Results reveal a multifractal spectrum and critical exponents, aligning with field-theory predictions.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Fractals

Background:

  • Percolation theory describes random networks.
  • Self-avoiding walks model paths that do not intersect.
  • Multifractality characterizes systems with varying scaling properties.

Purpose of the Study:

  • Investigate self-avoiding walks on percolation cluster backbones.
  • Analyze the multifractal spectrum of these walks.
  • Determine critical exponents and compare with theoretical predictions.

Main Methods:

  • Numerical simulations in dimensions d=2, 3, and 4.
  • Analysis of scaling laws for higher moments of visited sites.
  • Comparison with field-theoretical epsilon-expansion (epsilon=6-d).

Main Results:

  • The full multifractal spectrum of singularities was observed.
  • Estimates for critical exponents governing scaling laws were obtained.
  • Results show good correspondence with the epsilon-expansion.

Conclusions:

  • Numerical simulations confirm multifractal behavior of self-avoiding walks on percolation backbones.
  • The study validates theoretical predictions in different spatial dimensions.
  • This work provides insights into the complex scaling properties of disordered systems.