The quark-meson model and the phase diagram of QCD

I discuss the QCD phase diagram in the context of the linear quark-meson model with two flavours, using the exact renormalization group. I first give a pedagogical derivation of the qualitative features of the phase diagram based on mean field theory. Then I summarize how the the universality classes of the second-order phase transitions can be determined through the exact renormalization group. For non-zero quark masses I explain how the universal equation of state of the Ising universality class can be used in order to describe the physical behaviour near the critical point. The effective exponents that parametrize the growth of physical quantities, such as the correlation length, are given by combinations of the critical exponents of the Ising class that depend on the path along which the critical point is approached. In general the critical region, in which such quantities become large, is smaller than naively expected.