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Percolation on two- and three-dimensional lattices.

P H L Martins1, J A Plascak

  • 1Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte, MG, Brazil. phlm@fisica.ufgm.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 6, 2003
PubMed
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This study uses an efficient Monte Carlo algorithm to analyze percolation problems on various lattices. Researchers obtained accurate critical concentration and correlation exponent values, confirming universality in wrapping probabilities.

Area of Science:

  • Computational Physics
  • Statistical Mechanics
  • Materials Science

Background:

  • Percolation theory studies the formation of connected clusters in random systems.
  • Efficient algorithms are crucial for accurate simulations of complex lattice structures.
  • Understanding critical phenomena in disordered materials is essential for various applications.

Purpose of the Study:

  • To apply a novel Monte Carlo algorithm for simulating site and bond percolation.
  • To determine critical parameters like wrapping probabilities and correlation length exponents.
  • To investigate universality in percolation phenomena across different lattice types.

Main Methods:

  • Utilized the Newman-Ziff Monte Carlo algorithm for high efficiency.
  • Simulated site and bond percolation on 2D and 3D lattices (square, simple cubic, HCP, hexagonal).

Related Experiment Videos

  • Analyzed wrapping probabilities, correlation length critical exponent, and critical concentration.

    • Main Results:

    • Achieved accurate results for critical concentration and correlation length exponent with small systems.
    • Obtained reliable wrapping probabilities across diverse lattice structures.
    • Confirmed the universal nature of wrapping probabilities in site and bond percolation.

    Conclusions:

    • The Newman-Ziff algorithm provides an efficient and accurate method for percolation studies.
    • Results demonstrate the universality of percolation critical phenomena.
    • The study offers valuable insights into the behavior of disordered systems.