  We show that the dilute Fermi gas quantum critical universality class
quantitatively describes the Mott/metal crossover of the two-dimensional
Hubbard model for temperatures somewhat less than (roughly half) the tunneling
but much greater than (roughly twice) the superexchange energy. We calculate
the observables expected to be universal near the transition --- density and
compressibility --- with numerically exact determinantal quantum Monte Carlo.
We find they are universal functions of the chemical potential. Despite arising
from the strongly correlated regime of the Hubbard model, these functions are
given by the weakly interacting, dilute Fermi gas model. These observables and
their derivatives are the only expected universal static observables of this
universality class, which we also confirm by verifying there is no scaling
collapse of the kinetic energy, fraction of doubly occupied sites, and nearest
neighbor spin correlations. Our work resolves the universality class of the
intermediate temperature Mott/metal crossover, which had alternatively been
proposed to be described by more exotic theories. However, in the presence of a
Zeeman magnetic field, we find that interplay of spin with itinerant charge can
lead to physics beyond the dilute Fermi gas universality class.
