Differences

This shows you the differences between two versions of the page.

--- percolation [2021/05/05 05:17]
Scott Lawrence [Lattice theories]
+++ percolation [2021/05/05 19:06] (current)
Scott Lawrence [Bethe lattice]
@@ Line 42: / Line 42: @@
 ===== Bethe lattice =====
-The Bethe lattice can be thought of as the $d\rightarrow\infty$ 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 $p_c = (z-1)^{-1}$.
 ===== Related theories =====

CFT Zoo