Exact site percolation thresholds using a site-to-bond transformation and the star-triangle transformation.

  title={Exact site percolation thresholds using a site-to-bond transformation and the star-triangle transformation.},
  author={Christian R Scullard},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={73 1 Pt 2},
  • C. Scullard
  • Published 16 July 2005
  • Mathematics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
I construct a two-dimensional lattice on which the inhomogeneous site percolation threshold is exactly calculable and use this result to find two more lattices on which the site thresholds can be determined. The primary lattice studied here, the "martini lattice," is a hexagonal lattice with every second site transformed into a triangle. The site threshold of this lattice is found to be 0.764826..., i.e., the solution to p4 - 3p3 + 1 = 0, while the others have (square root 5 - 1)/2 (the inverse… 

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