  Progress in the understanding of quantum critical properties of itinerant
electrons has been hindered by the lack of effective models which are amenable
to controlled analytical and numerically exact calculations. Here we establish
that the disorder driven semimetal to metal quantum phase transition of three
dimensional massless Dirac fermions could serve as a paradigmatic toy model for
studying itinerant quantum criticality, which is solved in this work by exact
numerical and approximate field theoretic calculations. As a result, we
establish the robust existence of a non-Gaussian universality class, and also
construct the relevant low energy effective field theory that could guide the
understanding of quantum critical scaling for many strange metals. Using the
kernel polynomial method (KPM), we provide numerical results for the calculated
dynamical exponent ($z$) and correlation length exponent ($\nu$) for the
disorder-driven semimetal (SM) to diffusive metal (DM) quantum phase transition
at the Dirac point for several types of disorder, establishing its universal
nature and obtaining the numerical scaling functions in agreement with our
field theoretical analysis.
