Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Percolation threshold

  1. Jun 26, 2008 #1
    i am having some trouble understanding the meaning of what a percolation threshold is [tex] p_{c}[/tex].
    apparently on triangular lattices a threshold of 0.5 is the result on any sized lattice.
    however i can definitely think of a way to fill in half the points on a triangle lattice and not have it span across the lattice.
    similarly, one could make a zig zag line of connected sites to span a lattice without using anywhere near 1/2 the points. so is the percolation threshold a number at which you can expect to see percolation?

    all the books im reading seem to say that above it everything has a percolating net and below it there are no possible percolating nets.

    thanks a lot,

    josh S
  2. jcsd
  3. Jul 7, 2008 #2
    well in case anyone was wondering, the percolation threshold is the probability with which you need to fill in the nodes on a lattice so that in the limit of an infinite lattice, there is a non zero chance that you will have a spanning cluster going across it. for example, one could construct a spanning cluster across an infinite lattice by connecting a line of edges across the whole thing and in this example the probability you fill the lattice with is 0 (one row/infinite rows) but the probability of this happening is so low that it does not survive in the infinite limit.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook