Monte Carlo studies of percolation phenomena for a simple cubic lattice

Amit Sur, Joel L. Lebowitz, J. Marro, M. H. Kalos, S. Kirkpatrick

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The site-percolation problem on a simple cubic lattice is studied by the Monte Carlo method. By combining results for periodic lattices of different sizes through the use of finite-size scaling theory we obtain good estimates for pc (0.3115±0.0005), β (0.41±0.01), γ (1.6±0.1), and ν(0.8±0.1). These results are consistent with other studies. The shape of the clusters is also studied. The average "surface area" for clusters of size k is found to be close to its maximal value for the low-concentration region as well as for the critical region. The percentage of particles in clusters of different sizes k is found to have an exponential tail for large values of k for P <pc. For p >pc there is too much scatter in the data to draw firm conclusions about the size distribution.

Original languageEnglish (US)
Pages (from-to)345-353
Number of pages9
JournalJournal of Statistical Physics
Issue number5
StatePublished - Nov 1976
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Monte Carlo method
  • Site percolation
  • critical exponents
  • finite-size scaling
  • percolation threshold


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