I am not completely sure that this question is appropriate for this mathematical site. But since in the past I did get on MO couple of times nice answers to rather physical questions, I will try. Sorry if it is irrelevant here.
Some time ago I started to read basic things about conformal field theory. One of the basic examples there is the Ising model. It is characterized by certain specific collection of fields on the plane acted by the Virasoro algebra with certain central charge, and by a specific operator product expansion. In the conformal fields literature I read it is claimed that this model comes from the statistical mechanics.
In the literature on statistical mechanics what is called the Ising model is something completely different: one fixes a discrete lattice on the plane, and there is just one field which attaches numbers $\pm 1$ to each vertex of the lattice. (At the beginning I was not even sure that it is the same model of the same Ising :-))
As far as I heard there is a notion of scaling limit when the lattice spacing tends to zero. At this limit (at the critical temperature?) some important quantities (correlation functions?) converge to a limit. My guess is that this scaling limit should be somehow relevant to connect the two Ising models I mentioned above.
Question. Is there a good place to read about explicit relation between the two Ising models? In particular I would be interested to understand how to obtain the operator product expansion and the central charge starting from the statistical mechanics description.