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Simple algorithm to test for linking to Wilson loops in percolation.

Robert M Ziff1

  • 1Michigan Center for Theoretical Physics, and Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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A new algorithm tests if loops in percolation clusters connect to a reference loop. The method was validated at criticality in 2D and 3D, matching theoretical predictions.

Area of Science:

  • Statistical Physics
  • Computational Physics
  • Network Science

Background:

  • Percolation theory studies the formation of connected clusters in random systems.
  • Understanding loop structures in these clusters is crucial for various physical phenomena.
  • Previous work explored loop connectivity in the context of gauge theory.

Purpose of the Study:

  • To develop and test a novel algorithm for detecting loop connectivity in percolation clusters.
  • To investigate if loops in percolation clusters link to a fixed reference loop.
  • To validate the algorithm's performance at the critical point in different dimensions.

Main Methods:

  • Development of a simple burning or epidemic-type algorithm.
  • Application of the algorithm to percolation clusters at criticality.

Related Experiment Videos

  • Testing in both two-dimensional and three-dimensional lattice systems.

    • Main Results:

    • The algorithm successfully identifies loop connectivity in percolation clusters.
    • Performance at criticality in two dimensions aligns with theoretical predictions.
    • Behavior in three dimensions was also analyzed and found consistent.

    Conclusions:

    • The developed algorithm provides a viable method for studying loop structures in percolation.
    • The findings support theoretical expectations regarding loop behavior at criticality.
    • This approach can be extended to further investigate complex network properties.