  Quantum chromodynamics has a rather complicated phase structure. The finite
temperature, chiral phase structure depends on the number of flavours and to a
large extent on the particular values of the fermion masses. For two massless
flavours there is a true second order transition. It has been argued that this
transition belongs to the universality class of the three-dimensional O(4) spin
model. The arguments have been questioned recently, and the transition was
claimed to be mean field behaved. In this lecture we discuss this issue at the
example of the three-dimensional, parity symmetric Gross-Neveu model at finite
temperature, with a large number N of fermions. At zero temperature there is a
phase where parity is spontaneously broken. At finite temperature, this model
has a parity restoring second order transition. It reveals considerable
similarity to the QCD chiral phase transition. There are related questions here
concerning the universality class. We solve this problem essentially by means
of the following methods: Large N expansion, dimensional reduction in the
framework of quantum field theory, and high order convergent series expansions
about disordered lattice systems.
