 98740 Raphael Cerf, Emilio N.M. Cirillo
 Finite size scaling in threedimensional bootstrap percolation
(42K, LaTeX file)
Dec 4, 98

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. 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 threedimensional 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.
 Files:
98740.src(
98740.keywords ,
bootstrap.tex )