====== Self-avoiding walk ======

{{tag>logarithmic non-unitary 2d 3d}}

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 model is an example of a logarithmic CFT, which are non-unitarity.

===== External links =====

  * [[https://en.wikipedia.org/wiki/Self-avoiding walk|Wikipedia]]
  * see[[https://arxiv.org/abs/cond-mat/0209638|Cardy's notes]] on SAWs from a physics point of view
  * see [[https://arxiv.org/abs/1206.2092|1206.2092]] for lectures on SAWs from a mathematical viewpoint
  * see [[https://arxiv.org/abs/1605.03959|1605.03959]] on logarithmic CFTs for a discussion on the $O(0)$ model