Direct connection between statistical physics and string theory?

Question

I would like to think via standard transitivity arguments that there should be a deep connection between String theory and Statistical Physics. 

   Why?

  Statistical Physics $\rightarrow$ QFT

   
  2d QFT $\rightarrow$ String theory
 

  Statistical Physics $\rightarrow$ String theory ?

It came across my mind, and I thought I would ask. It would just be cool to know how such a connection is  established  directly from string theory to statistical mechanics without passing through standard quantum field theory arguments or if it can be done
   

Comments

There are plenty of 2d statistical systems which are understood by "string" methods, this is nearly all the 1980s physics. It started with the string-inspired conformal field theory paper of Belavin, Polyakov, Zamolodchikov, and the literature is reviewed, and there are textbooks.

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just to be sure this is the paper right?

http://users.physik.fu-berlin.de/~kamecke/ps/BPZ.pdf

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Yeah, that's the one. It's a classic even among the classics, it's arguably the greatest paper in 1980s physics, one of the greatest papers ever written. I think it's going to win the Nobel prize soon, it probably would have won already if they weren't Soviet.