The crossover from 2D to 3D percolation: theory and numerical simulations.

@article{Sotta2003TheCF,
  title={The crossover from 2D to 3D percolation: theory and numerical simulations.},
  author={Paul Sotta and D. Long},
  journal={The European physical journal. E, Soft matter},
  year={2003},
  volume={11 4},
  pages={375-87}
}
We describe here the crossover between 2D and 3D percolation, which we do on cubic and square lattices. As in all problems of critical phenomena, the quantities of interest can be expressed as power laws of /p-pc(h)/, where pc(h) and h are the percolation threshold and the thickness of the film, respectively. When these quantities are considered on the scale of the thickness h of the films, the corresponding numerical prefactors are of order one. However, for many problems, the scale of… CONTINUE READING