  Large-N expansions and computer simulations indicate that the universality
class of the finite temperature chiral symmetry restoration transition in the
3D Gross-Neveu model is mean field theory. This is a counterexample to the
standard 'sigma model' scenario which predicts the 2D Ising model universality
class. We trace the breakdown of the standard scenario (dimensional reduction
and universality) to the absence of canonical scalar fields in the model. We
point out that our results could be generic for theories with dynamical
symmetry breaking, such as Quantum Chromodynamics.
