  Four-fermi models in dimensionality $2<d<4$ exhibit an ultra-violet stable
renormalization group fixed point at a strong value of the coupling constant
where chiral symmetry is spontaneously broken. The resulting field theory
describes relativistic fermions interacting non-trivially via exchange of
scalar bound states. We calculate the $O(1/N_f)$ corrections to this picture,
where $N_f$ is the number of fermion species, for a variety of models and
confirm their renormalizability to this order. A connection between
renormalizability and the hyperscaling relations between the theory's critical
exponents is made explicit. We present results of extensive numerical
simulations of the simplest model for $d=3$, performed using the hybrid Monte
Carlo algorithm on lattice sizes ranging from $8^3$ to $24^3$. For $N_f=12$
species of massless fermions we confirm the existence of a second order phase
transition where chiral symmetry is spontaneously broken. Using both direct
measurement and finite size scaling arguments we estimate the critical
exponents $\beta$, $\gamma$, $\nu$ and $\delta$. We also investigate symmetry
restoration at non-zero temperature, and the scalar two-point correlation
function in the vicinity of the bulk transition. All our results are in
excellent agreement with analytic predictions, and support the contention that
the $1/N_f$ expansion is accurate for this class of models.
