Section 2
The free fermion (Ising) model

I introduce the Ising model as a first example of a conformal field theory (CFT), though we are not yet in a position to discuss all defining properties of CFTs. However, we can already make sense out of the representation theory of the Virasoro algebra at central charge c=1/2, and this allows us to understand some important aspects of the Ising model. I use it to introduce the notions of Fock space representations, unitary and lowest weight representations of the Virasoro algebra. The discussion of unitarity naturally leads to a first mention of minimal models, and the Ising model is the simplest non-trivial minimal model. All minimal models are conjectured to describe actual physical systems, namely phase transitions of second order, and I allow myself a short digression to motivate these ideas. I also write out the modular invariant partition function of the Ising model, again to introduce more general notions like the Jacobi theta functions, Poisson resummation and modular transformations.