Finite size scaling in three-dimensional bootstrap percolation
| dc.creator | Cerf, Raphael | |
| dc.creator | Cirillo, Emilio N. M. | |
| dc.date | 1998-12-04 | |
| dc.date.accessioned | 2026-07-07T03:12:18Z | |
| dc.date.available | 2026-07-07T03:12:18Z | |
| dc.description | We consider the problem of bootstrap percolation on a three dimensional lattice and we study its finite size scaling behavior. Bootstrap percolation is an example of Cellular Automata defined on the $d$-dimensional lattice $\{1,2,...,L\}^d$ in which each site can be empty or occupied by a single particle; in the starting configuration each site is occupied with probability $p$, occupied sites remain occupied for ever, while empty sites are occupied by a particle if at least $\ell$ among their $2d$ nearest neighbor sites are occupied. When $d$ is fixed, the most interesting case is the one $\ell=d$: this is a sort of threshold, in the sense that the critical probability $p_c$ for the dynamics on the infinite lattice ${\Bbb Z}^d$ switches from zero to one when this limit is crossed. Finite size effects in the three-dimensional case are already known in the cases $\ell\le 2$: in this paper we discuss the case $\ell=3$ and we show that the finite size scaling function for this problem is of the form $f(L)={\mathrm{const}}/\ln\ln L$. We prove a conjecture proposed by A.C.D. van Enter. | |
| dc.description | 18 pages, LaTeX file, no figure | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9812077 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9812077 | |
| dc.identifier | The Annals of Probability, 27, 1833-1850 (1999) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/28857 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Finite size scaling in three-dimensional bootstrap percolation | |
| dc.type | text |