Bootstrap percolation transitions on real lattices

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.