Critical percolation in high dimensions.

  title={Critical percolation in high dimensions.},
  author={Peter Grassberger},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={67 3 Pt 2},
  • Peter Grassberger
  • Published 2003 in
    Physical review. E, Statistical, nonlinear, and…
We present Monte Carlo estimates for site and bond percolation thresholds in simple hypercubic lattices with 4-13 dimensions. For d<6 they are preliminary, for d>or =6 they are between 20 and 10(4) times more precise than the best previous estimates. This was achieved by three ingredients: (i) simple and fast hashing that allowed us to simulate clusters of millions of sites on computers with less than 500 Mbytes memory; (ii) a histogram method that allowed us to obtain information for several p… CONTINUE READING