  Interacting theories of N relativistic fermion flavors in reducible spinor
representations in 2+1 spacetime dimensions are formulated on a lattice using
domain wall fermions (DWF), for which a U(2N) global symmetry is recovered in
the limit that the wall separation $L_s$ is made large. The Gross-Neveu (GN)
model is studied in the large-N limit and an exponential acceleration of
convergence to the large-$L_s$ limit is demonstrated if the usual
parity-invariant mass $m\bar\psi\psi$ is replaced by the U(2N)-equivalent
$im_3\bar\psi\gamma_3\psi$. The GN model and two lattice variants of the
Thirring model are simulated for N = 2 using a hybrid Monte Carlo algorithm,
and studies made of the symmetry-breaking bilinear condensate and its
associated susceptibility, the axial Ward identity, and the mass spectrum of
both fermion and meson excitations. Comparisons are made with existing results
obtained using staggered fermions. For the GN model a symmetry-breaking phase
transition is observed, the Ward identity is recovered, and the spectrum found
to be consistent with large-N expectations. There appears to be no obstruction
to the study of critical UV fixed-point physics using DWF. For the Thirring
model the Ward identity is not recovered, the spectroscopy measurements are
inconclusive, and no symmetry breaking is observed all the way up to the
effective strong coupling limit. This is consistent with a critical Thirring
flavor number $N_c<2$, contradicting earlier staggered fermion results.
