  We argue that theories with fundamental fermions which undergo chiral
symmetry breaking have several universal features which are qualitatively
different than those of theories with fundamental scalars. Several bounds on
the critical indices $\delta$ and $\eta$ follow. We observe that in four
dimensions the logarithmic scaling violations enter into the Equation of State
of scalar theories, such as $\lambda\phi^4$, and fermionic models, such as
Nambu-Jona-Lasinio, in qualitatively different ways. These observations lead to
useful approaches for analyzing lattice simulations of a wide class of model
field theories. Our results imply that $\lambda\phi^4$ {\it cannot} be a good
guide to understanding the possible triviality of spinor $QED$.
