  We study static and dynamical critical phenomena of chiral symmetry breaking
in a two-flavor Nambu--Jona-Lasinio constituent quark model. We obtain the
low-energy effective action for scalar and pseudoscalar degrees of freedom to
lowest order in quark loops and to quadratic order in the meson fluctuations
around the mean field. The \emph{static} limit of critical phenomena is shown
to be described by a Ginzburg-Landau effective action including \emph{spatial}
gradients. Hence \emph{static} critical phenomena is described by the
universality class of the O(4) Heisenberg ferromagnet. \emph{Dynamical}
critical phenomena is studied by obtaining the equations of motion for pion
fluctuations. We find that for $T<T_c$ the are stable long-wavelength pion
excitations with dispersion relation $\omega_{\pi}(k)=k$ described by isolated
pion poles. The residue of the pion pole vanishes near $T_c$ as $Z \propto
1/|\ln(1-T/T_c)|$ and long-wavelength fluctuations are damped out by Landau
damping on a time scale $t_\mathrm{rel}(k)\propto 1/k$, reflecting
\emph{critical slowing down} of pion fluctuations near the critical point. At
the critical point, the pion propagator features mass shell logarithmic
divergences which we conjecture to be the harbinger of a (large) dynamical
anomalous dimension. We find that while the \emph{classical spinodal} line
coincides with that of the Ginzburg-Landau theory, the growth rate of
long-wavelength spinodal fluctuations has a richer wavelength dependence as a
consequence of Landau damping. We argue that Landau damping prevents a
\emph{local} low energy effective action in terms of a derivative expansion in
real time.
