  Results of a lattice field theory simulation of the single-flavor Thirring
model in 2+1 spacetime dimensions are presented. The lattice model is
formulated using domain wall fermions as a means to recover the correct U(2)
symmetries of the continuum model in the limit where wall separation
$L_s\to\infty$. Simulations on $12^3, 16^3\times L_s$, varying self-interaction
strength $g^2$ and bare mass $m$ are performed with $L_s = 8, \ldots 48$, and
the results for the bilinear condensate $\langle\bar\psi\psi\rangle$ fitted to
a model equation of state assuming a U(2)$\to$U(1)$\otimes$U(1)
symmetry-breaking phase transition at a critical $g_c^2$. First estimates for
$g^{-2}a$ and critical exponents are presented, showing small but significant
departures from mean-field values. The results confirm that a symmetry-breaking
transition does exist and therefore the critical number of flavors for the
Thirring model $N_c > 1$. Results for both condensate and associated
susceptibility are also obtained in the broken phase on $16^3\times48$,
suggesting that here the $L_s\to\infty$ extrapolation is not yet under control.
We also present results obtained with the associated 2+1$d$ truncated overlap
operator DOL demonstrating exponential localisation, a necessary condition for
the recovery of U(2) global symmetry, but that recovery of the Ginsparg-Wilson
condition as $L_s\to\infty$ is extremely slow in the broken phase.
