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Bootstrap percolation transitions on real lattices

, and . Journal of Physics C: Solid State Physics, 14 (22): 3187-3194 (1981)
DOI: 10.1088/0022-3719/14/22/013

Abstract

In bootstrap percolation, a fraction p of the sites of a lattice is first randomly occupied, and then all occupied sites with fewer than a given integral number m of occupied neighbours are successively culled (rendered unoccupied) until either (a) a configuration of occupied sites, each with m or more occupied neighbours, ensues or (b) all sites of the lattice are vacated. The authors treat this problem as a function of m on square, triangular and cubic lattices by computer simulation. Various types of percolation transitions are discovered, including some which are discontinuous and some which are continuous but characterised by non-universal critical exponents.

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Bootstrap percolation transitions on real lattices

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