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Bootstrap Percolation: visualizations and applications Joan Adler 1 and Uri Lev 2

Summary: Bootstrap Percolation: visualizations and applications
Joan Adler 1 and Uri Lev 2
1 Department of Physics, Technion-IIT, 32000 Haifa, Israel
and 2 Department of Materials Engineering, Technion-IIT, 32000 Haifa, Israel
(June 3, 2003)
Bootstrap percolation models describe systems as diverse as magnetic mate-
rials, uid ow in rocks and computer storage systems. The models have a
common feature of requiring not just a simple connectivity of neighbouring
sites, but rather an environment of other suitably occupied sites. Di erent
applications as well as the connection with the mathematical literarure on
these models is presented. Visualizations that show the compact nature of
the clusters are provided.
In Bootstrap Percolation (BP) [1] the lattice is occupied randomly with probability p,
and then all sites that do not have at least m neighbours are iteratively removed. For
m = 1 isolated sites are removed and for m = 2 both isolated sites and dangling ends are
removed. For m = 3 and above the situation becomes interesting and lattice dependent and
is currently quite hot amongst probablists. For suĂciently high m, no occupied sites remain
for an in nite lattice, and the interest is in the scaling as a function of system size.


Source: Adler, Joan - Physics Department, Technion, Israel Institute of Technology


Collections: Physics