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I'm a math grad student interested in statistical physics. I notice (e.g. in this book) that physicists are interested in random walks on percolation clusters and other fractals, and this has something to do with material properties of "disordered media." This seems very interesting, but I don't have the background to know what is supposed to happen in "ordered media," as it were, so starting off with "disordered media" is absurd.

I realize that now (or after I pass my qualifying exams...) is the time to start cracking open basic condensed matter physics texts to learn this material and I will do that.

For now, if anyone can suggest references that will give me a sense of what random walks on $\mathbb{Z}^{d}$ (with deterministic transition probabilities) have to do with condensed matter physics, that would be great. Basically, I would like to be able to translate from purely mathatematical facts about random walks to their physical interpretations and to have a better understanding of typical physical scenarios in which random walks model transport phenomena.

Qmechanic
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fourierwho
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    Welcome to Physics Stack Exchange! This is an excellent site for physics questions and answers. Note that we have certain guidelines to keep the quality high. This post is pretty broad. Some times, questions that really are too broad to be answered are closed, so if that happens, just edit the post to make it more specific. In fact, I'd recommend doing that anyway. You're essentially asking for references showing where random walks come up in condensed matter physics; there are so many that it might help to specify in some way. – DanielSank Jan 24 '17 at 23:55
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    Brownian motion is a "classic"? https://en.wikipedia.org/wiki/Brownian_motion – JMLCarter Jan 25 '17 at 00:43
  • -1. Have you done any research? eg have you googled "diffusion in ordered media" or even just "random walks in physics"? – sammy gerbil Jan 25 '17 at 02:17
  • Good lecture notes on the topic: http://physics.ucsd.edu/~mcgreevy/w16/index.html . Some facts: Thermal classical and quantum systems have a very specific $e^{-\beta E}$ distribution; self avoiding random walks occur as the "n->0 limit" of the O(n) model; cale invariance occurs at critical points of thermal systems (giving rise to fractals); the Ising model of ferromagnetism has pretty clear relations to percolation (see this question); self avoiding random walks have a direct connection to polymer chains (experimentally measurable!) –  Jan 25 '17 at 05:12

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