Introduction to Percolation Theory

Stauffer, D., & Aharony, A. (1994). Introduction to Percolation Theory. Taylor & Francis.

Type

Book

Intellectual base

Textbook

Year

1994

Link

https://www.routledge.com/Introduction-To-Percolation-Theory-Second-Edition/Stauffer-Aharony/p/book/9780748402533

Cited from

chemistry_materials, pharmacology_toxicology, physics

Cited by

5 citations across 5 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Percolation
  • The canonical mathematical case is bond or site percolation on a lattice, each bond or site independently present with probability \(p\), but the same structural behavior extends to random graphs, configuration models, spatial random networks, and continuum percolation, with substrate-dependent values of \(p_c\) but the identical qualitative phase transition.
• Percolation Threshold
  • Materials and chemistry — porous-rock permeability appears suddenly when pore connectivity exceeds threshold; conductive-filler composites become conductive when the filler fraction crosses \(p_c\); gelation is exactly the point at which crosslinks first span a polymer solution.
• Threshold

  • This sourceTaylor & Francis. — Mathematical characterization of percolation threshold in physics.

• Threshold-Driven Order Emergence
  • Percolation theory provides another canonical formal example.

Mechanisms

• Staged Link-Density Trial
  • Its failure mode is false precision at a sharp threshold: near a percolation point, small-sample and finite-size effects make the estimate jumpy, so a tidy single number oversells how well the threshold is actually known.

    This sourceShows that finite system size can shift the apparent percolation threshold away from its infinite-system value.

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