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self_avoiding_walk [2021/11/13 13:23] Brian McPeak [Self-avoiding walk] |
self_avoiding_walk [2021/11/13 13:29] (current) Brian McPeak [External links] |
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| A self-avoiding random walk (or self-avoiding walk, or SAW) is a path on a $d$-dimensional lattice in $\mathbb{Z}^d$ which never visits the same point more than once. As a statistical model, they are defined as the set of all such paths with length $n$ weighted with equal probability. A number of questions concerning their behavior as $n \to \infty$ are still open, and the models display a rich variety of critical behavior. | A self-avoiding random walk (or self-avoiding walk, or SAW) is a path on a $d$-dimensional lattice in $\mathbb{Z}^d$ which never visits the same point more than once. As a statistical model, they are defined as the set of all such paths with length $n$ weighted with equal probability. A number of questions concerning their behavior as $n \to \infty$ are still open, and the models display a rich variety of critical behavior. | ||
| - | This is the $n\rightarrow 0$ specialization of the [[on_model]]. | + | This is the $n\rightarrow 0$ specialization of the [[on_model]]. This model is an example of a logarithmic CFT, which are non-unitarity. |
| ===== External links ===== | ===== External links ===== | ||
| * [[https:// | * [[https:// | ||
| - | * see [[https:// | + | |
| - | * see [[https:// | + | |
| + | * see [[https:// | ||