%0 Journal Article %1 Aizenman1988Metastability %A Aizenman, M. %A Lebowitz, J. L. %D 1988 %J Journal of Physics A: Mathematical and General %K cellular\_automata, metastability, percolation finite-size bootstrap %N 19 %P 3801+ %R 10.1088/0305-4470/21/19/017 %T Metastability effects in bootstrap percolation %U http://dx.doi.org/10.1088/0305-4470/21/19/017 %V 21 %X 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<<1, at sites of Z d (d>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 =p 1 (d-1)/ln L. The driving mechanism is the capture of a 'critical droplet'. This behaviour is analogous to the decay of a metastable state near a first-order phase transition, for which the analysis offers some suggestive ideas.

@article{Aizenman1988Metastability, 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<<1, at sites of Z d (d>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 =p 1 (d-1)/ln L. The driving mechanism is the capture of a 'critical droplet'. This behaviour is analogous to the decay of a metastable state near a first-order phase transition, for which the analysis offers some suggestive ideas.}}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Aizenman, M. and Lebowitz, J. L.}, biburl = {https://www.bibsonomy.org/bibtex/21d10806139bfcc5d1ee8f553217fad44/nonancourt}, citeulike-article-id = {9319877}, citeulike-linkout-0 = {http://dx.doi.org/10.1088/0305-4470/21/19/017}, citeulike-linkout-1 = {http://iopscience.iop.org/0305-4470/21/19/017}, day = 07, doi = {10.1088/0305-4470/21/19/017}, interhash = {2f716c8dc440baeb9f9470ffd1cc1cfd}, intrahash = {1d10806139bfcc5d1ee8f553217fad44}, issn = {0305-4470}, journal = {Journal of Physics A: Mathematical and General}, keywords = {cellular\_automata, metastability, percolation finite-size bootstrap}, month = oct, number = 19, pages = {3801+}, posted-at = {2011-05-20 16:06:03}, priority = {2}, timestamp = {2019-08-23T10:58:50.000+0200}, title = {{Metastability effects in bootstrap percolation}}, url = {http://dx.doi.org/10.1088/0305-4470/21/19/017}, volume = 21, year = 1988 }