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Percolation with long-range correlated disorder.

K J Schrenk1, N Posé1, J J Kranz1

  • 1Computational Physics for Engineering Materials, Institute for Building Materials, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland.

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This summary is machine-generated.

This study investigates long-range power-law correlated percolation using Monte Carlo simulations. Critical exponents were determined as functions of the Hurst exponent (H), revealing insights into spatial correlation effects on cluster properties and transport.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Materials Science

Background:

  • Percolation theory describes the formation of connected clusters in random systems.
  • Long-range correlations introduce complex spatial dependencies not captured by standard models.
  • Understanding these correlations is crucial for diverse fields, including disordered materials and network science.

Purpose of the Study:

  • To investigate long-range power-law correlated percolation.
  • To determine static and dynamic critical exponents as functions of the Hurst exponent (H).
  • To analyze the structural and transport properties of the largest cluster.

Main Methods:

  • Monte Carlo simulations were employed to model percolation phenomena.
  • The Hurst exponent (H) was used to quantify the degree of spatial correlation.
  • Analysis included fractal dimension, cluster size distribution, perimeters, shortest paths, backbone, red sites, and conductivity.

Main Results:

  • Static and dynamic critical exponents were systematically obtained as functions of H.
  • The study characterized the fractal dimension and scaling behavior of the largest cluster.
  • Expressions for the functional dependence of critical exponents on H were proposed.

Conclusions:

  • The Hurst exponent (H) significantly influences critical exponents in long-range correlated percolation.
  • Detailed insights into the inner structure and transport properties of the largest cluster were provided.
  • The findings offer a framework for understanding correlated systems in various scientific disciplines.