  The Thirring model in 2+1 spacetime dimensions, in which $N$ flavors of
relativistic fermion interact via a contact interaction between conserved
fermion currents, is studied using lattice field theory simulations employing
domain wall fermions, which furnish the correct U(2N) global symmetry in the
limit that the wall separation $L_s\to\infty$. Attention is focussed on the
issue of spontaneous symmetry breakdown via a non-vanishing fermion bilinear
condensate $\langle\bar\psi\psi\rangle\not=0$. Results from quenched
simulations are presented demonstrating that a non-zero condensate does indeed
form over a range of couplings, provided simulation results are first
extrapolated to the $L_s\to\infty$ limit. Next, results from simulations with
$N=1$ using an RHMC algorithm demonstrate that U(2) symmetry is unbroken at
weak coupling but plausibly broken at strong coupling. Correlators of mesons
with spin zero are consistent with the Goldstone spectrum expected from
U(2)$\to$U(1)$\otimes$U(1). We infer the existence of a symmetry-breaking phase
transition at some finite coupling, and combine this with previous simulation
results to deduce that the critical number of flavors for the existence of a
quantum critical point in the Thirring model satisfies $0<N_c<2$, with strong
evidence that in fact $N_c>1$.
