  We study the critical phenomena of the dynamical transition from a metastable
state to a stable state in the model of first-order phase transition via two
different triggering mechanisms. Three universal stages during the fully
nonlinear evolution are extracted. On the one side, by perturbing the scalar
source, an isolated seed nucleus is injected into an initial homogeneous state
in the supercooled region. For critical parameters of the seed nucleus, the
real-time dynamics reveal that the system will converge to a critically
unstable state. For supercritical parameters, the system exhibits a phase
separation, while for subcritical parameters falls back to homogeneous. The
shape independence of the seed nucleus is also investigated, which implies that
the critical phenomena are universal. On the other side, we propose a novel
mechanism to render the critical phenomena via a collision of two gravitational
shock waves on the dual geometries. Specifying a collision velocity, the
initial system can be also attracted to a critically unstable state. Aside from
these dynamical constructions, we also quantitatively analyze the critical
nucleus preventing the system from reaching the final phase separation. We find
the depth of the critical nucleus increases almost linearly with the
temperature, which implies that the hotter the supercooled state is, the harder
for it to trigger phase separation.
