  We compute the temperature dependence of the antiferromagnetic order
parameter and the gap in the two dimensional Hubbard model at and close to half
filling. Our approach is based on truncations of an exact functional
renormalization group equation. The explicit use of composite bosonic degrees
of freedom permits a direct investigation of the ordered low temperature phase.
We show that the Mermin--Wagner theorem is not practically applicable for the
spontaneous breaking of the continuous spin symmetry in the antiferromagnetic
state. The critical behavior is dominated by the fluctuations of composite
Goldstone bosons.
