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@ARTICLE{Grassberger:840252,
      author       = {Grassberger, Peter and Hilário, Marcelo R. and
                      Sidoravicius, Vladas},
      title        = {{P}ercolation in {M}edia with {C}olumnar {D}isorder},
      journal      = {Journal of statistical physics},
      volume       = {168},
      number       = {4},
      issn         = {1572-9613},
      address      = {New York, NY [u.a.]},
      publisher    = {Springer Science + Business Media B.V.},
      reportid     = {FZJ-2017-07805},
      pages        = {731 - 745},
      year         = {2017},
      abstract     = {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.},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000406657400002},
      doi          = {10.1007/s10955-017-1826-7},
      url          = {https://juser.fz-juelich.de/record/840252},
}