TY  - JOUR
AU  - Grassberger, Peter
AU  - Hilário, Marcelo R.
AU  - Sidoravicius, Vladas
TI  - Percolation in Media with Columnar Disorder
JO  - Journal of statistical physics
VL  - 168
IS  - 4
SN  - 1572-9613
CY  - New York, NY [u.a.]
PB  - Springer Science + Business Media B.V.
M1  - FZJ-2017-07805
SP  - 731 - 745
PY  - 2017
AB  - We study a generalization of site percolation on a simple cubic lattice, where not only single sites are removed randomly, but also entire parallel columns of sites. We show that typical clusters near the percolation transition are very anisotropic, with different scaling exponents for the sizes parallel and perpendicular to the columns. Below the critical point there is a Griffiths phase where cluster size distributions and spanning probabilities in the direction parallel to the columns have power-law tails with continuously varying non-universal powers. This region is very similar to the Griffiths phase in subcritical directed percolation with frozen disorder in the preferred direction, and the proof follows essentially the same arguments as in that case. But in contrast to directed percolation in disordered media, the number of active (“growth”) sites in a growing cluster at criticality shows a power law, while the probability of a cluster to continue to grow shows logarithmic behavior.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000406657400002
DO  - DOI:10.1007/s10955-017-1826-7
UR  - https://juser.fz-juelich.de/record/840252
ER  -