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

  title={The crossover from 2D to 3D percolation: Theory and numerical simulations},
  author={Paul Sotta and Didier R. Long},
  journal={The European Physical Journal E},
  • P. SottaD. Long
  • Published 1 August 2003
  • Physics
  • The European Physical Journal E
Abstract.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 $\vert p-p_{\rm c}(h)\vert$, where $p_{\rm c}(h)$ 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… 

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