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Related Experiment Videos

Site percolation thresholds for Archimedean lattices.

P N Suding1, R M Ziff

  • 1Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

This study precisely calculates site percolation thresholds for eight Archimedean lattices using a novel simulation method. Results show a strong correlation with a generalized filling factor, improving accuracy over previous models.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Materials Science

Background:

  • Percolation theory is crucial for understanding phase transitions in disordered systems.
  • Archimedean lattices provide a framework for studying geometric properties of materials.
  • Accurate percolation thresholds are essential for predicting material behavior.

Purpose of the Study:

  • To determine precise site percolation thresholds for eight Archimedean lattices.
  • To investigate correlations between percolation thresholds and lattice properties.
  • To develop a more accurate predictive model for percolation phenomena.

Main Methods:

  • Utilized the hull-walk gradient-percolation simulation method.
  • Calculated critical percolation probabilities (p(c)) for specified lattices with high precision.

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  • Analyzed correlations using a generalized Scher-Zallen filling factor.

    • Main Results:

    • Precise p(c) values were obtained for eight Archimedean lattices, with errors around +/- 3 x 10(-6).
    • The result for the (3,12(2)) lattice aligns with its exact value.
    • A strong, nearly linear correlation was found between p(c) and the generalized filling factor for all 11 Archimedean lattices.

    Conclusions:

    • The hull-walk gradient-percolation method provides highly accurate site percolation thresholds.
    • The generalized Scher-Zallen filling factor offers a superior correlation for percolation thresholds compared to coordination number alone.
    • This work refines our understanding of percolation phenomena in various lattice structures.