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percolation [2021/05/05 19:06] – [Bethe lattice] Scott Lawrencepercolation [2021/05/05 19:06] (current) – [Bethe lattice] Scott Lawrence
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 The Bethe lattice can be thought of as the $d\rightarrow\infty$ lattice. It is the infinite tree in which each vertex has the same number ($z$ --- called the coordination number) of neighbors. Note that $z=1$ is invalid, and $z=2$ is just a one-dimensional lattice. The Bethe lattice can be thought of as the $d\rightarrow\infty$ lattice. It is the infinite tree in which each vertex has the same number ($z$ --- called the coordination number) of neighbors. Note that $z=1$ is invalid, and $z=2$ is just a one-dimensional lattice.
  
-As with many statistical models, percolation can be exactly solved on a Bethe lattice: see for instance [[https://web.mit.edu/ceder/publications/Percolation.pdf|these notes]]. The critical exponent is $\beta = 1$; the percolation threshold is $p_c = (z-1)^{-1}$+As with many statistical models, percolation can be exactly solved on a Bethe lattice: see for instance [[https://web.mit.edu/ceder/publications/Percolation.pdf|these notes]]. The critical exponent is $\beta = 1$; the percolation threshold is $p_c = (z-1)^{-1}$.
 ===== Related theories ===== ===== Related theories =====
  
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