I would like to read some of the physics literature on two-dimensional percolation, however in attempting this I have run into two problems. (1) Physics papers on percolation are (relatively) hard for me to locate, and when I do locate them I don't know which are the important ones I should read. (2) Given my lack of substantial background in mathematical physics, the physics papers I find are hard for me to read.
I have become interested in two-dimensional percolation since reading some of the (relatively) recent been spectacular progress in the (mathematical) theory of two-dimensional percolation due to Smirnov, Schramm, Lawler, Werner, and others (which confirms many conjectures from the physics literature,though many open questions still remain).
The best I currently can do is to look at references to the physics literature in mathematics papers on percolation. I am looking for:
- Specific outstanding physics papers about two-dimensional percolation which I should read.
- Useful tips for mathematicians trying to read such papers.
Thanks very much!
Best Answer
(1) Look first at the references in Schramm and Smironv and Lowler. They refer to some important physics papers. Also look at the survey of Langlands, Pouliot, Saint-Aubin, Conformal invariance in two-dimensional percolation. Bull. Amer. Math. Soc. (N.S.) 30 (1994), no. 1, 1–61. This is almost a "physics paper", but Langlands is a mathematician, and it has a lot of references on other physics papers.
The large book Geoffrey Grimmett, Percolation. Springer-Verlag, New York, 1989 is written for mathematicians, but has a lot of references on physicists.
(2) This is a special case of a more general question, "how can a mathematician read physicist's papers?" It is really VERY difficult (my own experience). There is no general answer. There are some papers written specially for mathematicians, for example, Harry Kesten, Percolation theory for mathematicians, Birkhäuser, Boston, Mass., 1982. iv+423 pp.
On the last questions: look at the papers of John Cardy which have "percolation" in their title. He is a physicist, and some of his papers are among the most important in the subject.
Useful tips? It will take too long to explain. Just read and practice. Use patience. Do not try to understand every word or every sentence. Eventually you will discover that some physicists write in more intelligible style than others. Look at mathematicians papers on the same subject and compare. You will eventually learn the meaning of some words in this way. But this is indeed difficult, for a mathematician to read physicists papers, there is no doubt about it.