  We study dynamical phase transitions from antiferromagnetic to paramagnetic
states driven by an interaction quench in the fermionic Hubbard model using the
nonequilibrium dynamical mean-field theory. We identify two dynamical
transition points where the relaxation behavior qualitatively changes: one
corresponds to the thermal phase transition at which the order parameter decays
critically slowly in a power law $\propto t^{-1/2}$, and the other is connected
to the existence of nonthermal antiferromagnetic order in systems with
effective temperature above the thermal critical temperature. The frequency of
the amplitude mode extrapolates to zero as one approaches the nonthermal
(quasi)critical point, and thermalization is significantly delayed by the
trapping in the nonthermal state. A slow relaxation of the nonthermal order is
followed by a faster thermalization process.
