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Percolation in a random environment.

Róbert Juhász1, Ferenc Iglói

  • 1Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary and Research Institute for Solid State Physics and Optics, H-1525 Budapest, P.O.Box 49, Hungary.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 7, 2003
PubMed
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This study examines bond percolation on a square lattice with correlated random probabilities. It reveals new random fixed points governing critical behavior, with exponents becoming exactly known at infinite randomness.

Area of Science:

  • Statistical physics
  • Complex systems

Background:

  • Percolation theory studies the connectivity of random networks.
  • Understanding critical phenomena in disordered systems is crucial.

Purpose of the Study:

  • Investigate bond percolation on a square lattice with perfectly correlated random probabilities.
  • Characterize the critical behavior under varying degrees of disorder.

Main Methods:

  • Scaling considerations.
  • Mapping to a random walk problem.
  • Monte Carlo simulations.

Main Results:

  • Identified new, random fixed points governing critical behavior.
  • Observed anisotropic scaling properties.

Related Experiment Videos

  • Found nonuniversal exponents for weaker disorder.
  • Demonstrated scaling into an infinite randomness fixed point for strong disorder.

    • Conclusions:

    • The critical behavior is governed by novel random fixed points.
    • The system exhibits distinct scaling regimes based on disorder strength.
    • Exact critical exponents are determined at the infinite randomness fixed point.