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Results of a lattice field theory simulation of the single-flavor Thirringmodel in 2+1 spacetime dimensions are presented. The lattice model isformulated 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-interactionstrength $g^2$ and bare mass $m$ are performed with $L_s = 8, \ldots 48$, andthe results for the bilinear condensate $\langle\bar\psi\psi\rangle$ fitted toa 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 significantdepartures from mean-field values. The results confirm that a symmetry-breakingtransition does exist and therefore the critical number of flavors for theThirring model $N_c > 1$. Results for both condensate and associatedsusceptibility 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 overlapoperator DOL demonstrating exponential localisation, a necessary condition forthe recovery of U(2) global symmetry, but that recovery of the Ginsparg-Wilsoncondition as $L_s\to\infty$ is extremely slow in the broken phase.

Critical Behaviour in the Single Flavor Thirring Model in 2+1d