Exact bond percolation thresholds in two dimensions

  title={Exact bond percolation thresholds in two dimensions},
  author={Robert M. Ziff and Christian R Scullard},
  journal={Journal of Physics A},
Recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices. Here we show how these results can be extended to other classes of graphs, significantly increasing the number and variety of solved problems. Any graph that can be decomposed into a certain arrangement of triangles, which we call self-dual, gives a class of lattices whose percolation thresholds can be found exactly by a recently introduced triangle–triangle transformation. We… 

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