  A model Vlasov--Poisson system is simulated close the point of marginal
stability, thus assuming only the wave-particle resonant interactions are
responsible for saturation, and shown to obey the power--law scaling of a
second-order phase transition. The set of critical exponents analogous to those
of the Ising universality class is calculated and shown to obey the Widom and
Rushbrooke scaling and Josephson's hyperscaling relations at the formal
dimensionality $d=5$ below the critical point at nonzero order parameter.
However, the two-point correlation function does not correspond to the
propagator of Euclidean quantum field theory, which is the Gaussian model for
the Ising universality class. Instead it corresponds to the propagator for the
fermionic {\it vector} field and to the {\it upper critical dimensionality}
$d_c=2$. This suggests criticality of collisionless Vlasov-Poisson systems as
representative of the {\it universality class} of critical phenomena of {\it a
fermionic} quantum field description.
