publication . Article . 1988

Metastability effects in bootstrap percolation

Michael Aizenman; Joel L. Lebowitz;
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  • Published: 07 Oct 1988 Journal: Journal of Physics A: Mathematical and General, volume 21, pages 3,801-3,813 (issn: 0305-4470, eissn: 1361-6447, Copyright policy)
  • Publisher: IOP Publishing
Abstract
Bootstrap percolation models, or equivalently certain types of cellular automata, exhibit interesting finite-volume effects. These are studied at a rigorous level. The authors find that for an initial configuration obtained by placing particles independently with probability p or=2), the density of the 'bootstrapped' (final) configurations in the sequence of cubes (-L/2, L/2)d typically undergoes an abrupt transition, as L is increased, from being close to 0 to the value 1. With L fixed at a large value, the mean final density as a function of p changes from 0 to 1 around a value which varies only slowly with L-the pertinent parameter being lambda =p1(d-1)/ln L....
Subjects
free text keywords: Mathematical Physics, General Physics and Astronomy, Statistical and Nonlinear Physics, Drop (liquid), Phase transition, Statistical physics, Mathematics, Cellular automaton, Discrete mathematics, Lambda, Metastability, Cube, Bootstrap percolation
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