UNIVERSALITY CLASS FOR BOOTSTRAP PERCOLATION WITHm=3ON THE CUBIC LATTICE

N. S. Branco () and Cristiano J. Silva
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N. S. Branco: Universidade Federal de Santa Catarina, Depto. de Física, 88040-900, Florianópolis, SC, Brazil
Cristiano J. Silva: Universidade Federal de Santa Catarina, Depto. de Física, 88040-900, Florianópolis, SC, Brazil

International Journal of Modern Physics C (IJMPC), 1999, vol. 10, issue 05, 921-930

Abstract: We study them = 3bootstrap percolation model on a cubic lattice, using Monte Carlo simulation and finite-size scaling techniques. In bootstrap percolation, sites on a lattice are considered occupied (present) or vacant (absent) with probabilitypor1-p, respectively. Occupied sites with less thanmoccupied first-neighbors are then rendered unoccupied; this culling process is repeated until a stable configuration is reached. We evaluate the percolation critical probability,pc, and both scaling powers,ypandyh, and, contrary to previous calculations, our results indicate that the model belongs to the same universality class as usual percolation (i.e.,m=0). The critical spanning probability,R(pc), is also numerically studied for systems with linear sizes ranging fromL=32up toL=480; the value we found,R(pc)=0.270±0.005, is the same as for usual percolation with free boundary conditions.

Keywords: Correlated percolation; Phase transition; Universality classes (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1142/S0129183199000711

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