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percolation [2021/04/13 21:15] Scott Lawrence [Related theories] |
percolation [2021/05/05 19:06] (current) Scott Lawrence [Bethe lattice] |
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===== Lattice theories ===== | ===== Lattice theories ===== | ||
- | Percolation can be defined as either bond or site percolation, | + | Percolation can be defined as either bond or site percolation, |
Because percolation is not a unitary CFT, there is no Hamiltonian lattice theory that flows to percolation in the IR. All lattices in this section are spacetime lattices. | Because percolation is not a unitary CFT, there is no Hamiltonian lattice theory that flows to percolation in the IR. All lattices in this section are spacetime lattices. | ||
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===== Bethe lattice ===== | ===== 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. |
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+ | As with many statistical models, percolation can be exactly solved on a Bethe lattice: see for instance [[https:// | ||
===== Related theories ===== | ===== Related theories ===== | ||