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Correlation length exponent in the three-dimensional fuse network.

Thomas Ramstad1, Jan Ø H Bakke, Johannes Bjelland

  • 1Department of Physics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 5, 2004
PubMed
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We measured the critical correlation length exponent (nu) in the 3D fuse model, finding nu=0.83+/-0.04. This differs from ordinary percolation

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • The fuse model is a crucial framework for understanding disordered systems.
  • Percolation theory describes the formation of connected clusters in random systems.
  • The critical correlation length exponent (nu) characterizes the scaling behavior near critical points.

Purpose of the Study:

  • To numerically determine the critical correlation length exponent (nu) in the three-dimensional fuse model.
  • To investigate the influence of broad threshold distributions on the system's critical behavior.
  • To compare the obtained exponent with that of ordinary percolation.

Main Methods:

  • Numerical simulations of the three-dimensional fuse model.
  • Utilizing broad threshold distributions to ensure the strong-disorder regime.

Related Experiment Videos

  • Analysis of survival probability fluctuations to extract the critical exponent.

    • Main Results:

    • The critical correlation length exponent was determined to be nu = 0.83 ± 0.04.
    • This value was obtained under conditions of broad threshold distributions, indicative of the strong-disorder regime.
    • The measured exponent differs significantly from the value of ordinary percolation (nu = 0.88).

    Conclusions:

    • The three-dimensional fuse model exhibits a distinct critical correlation length exponent compared to ordinary percolation.
    • The strong-disorder regime, achieved with broad threshold distributions, is essential for this observation.
    • These findings contribute to a deeper understanding of critical phenomena in disordered systems.