Critical scaling in the $N=1$ Thirring Model in $(2+1)d$

The Thirring model in 2+1$d$ with $N$ Dirac flavors can exhibit spontaneous U($2N)\to$U($N)\otimes$U($N$) breaking through fermion - antifermion condensation in the limit $m\to 0$. With no small parameter in play the symmetry-breaking dynamics is strongly-interacting and quantitative work requires a fermion formulation accurately capturing global symmetries. We present simulation results for $N=1$ obtained with Wilson kernel domain wall fermions on ${16}^3\times L_s$, with $L_s=24,\dots ,120$. The $L_s\to \mathrm{\infty }$ extrapolation of the bilinear condensate $⟨\bar{\psi }\psi ⟩$ as a function of coupling and bare mass is fitted to an empirical equation of state; the resulting critical exponents are significantly altered from previously obtained values, and for the first time resemble those emerging from analytic predictions based on approximate solutions to Schwinger-Dyson equations, consistent with a putative UV-stable renormalisation group fixed point. To address the non-perturbative issue of the value $N_c$ below which such a fixed point exists we present preliminary results obtained with $N=2$.