TITLE: How should a mathematician approach the physics literature concerning percolation?
QUESTION [11 upvotes]: 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!

REPLY [2 votes]: This is just one reference; by no means a comprehensive answer to your broad question.
This paper,

Jacob J.H. Simmons. "Logarithmic operator intervals in the boundary theory of critical percolation." Journal of Physics A: Mathematical and Theoretical 46, no. 49 (2013): 494015. (Journal link.)
  (Earlier arXiv abstract.)

uses conformal field
theory (CFT) "to probe the problems of critical two dimensional
percolation."
The author
calculates "crossing probabilities and expectation values of crossing cluster numbers" in hexagons for continuum percolation at criticality.

          


In the figure caption, "$O(n)$" refers to the $O(n)$ loop model,
referencing 

Domany E, Mukamel D, Nienhuis B and Schwimmer A 1981 Nucl. Phys. B190 279–287.