Critical behavior in the single flavor Thirring model in (2+1)D with Wilson kernel domain wall fermions

We present results of a lattice field theory simulation of the (2+1)D Thirring model with N=1 fermion flavors, using domain wall fermions. The model exhibits a U(2)-symmetry-breaking phase transition with the potential to define a UV-stable renormalization group fixed point. The novelty is the replacement of the Shamir kernel used in all previous work with the Wilson kernel, improving the action particularly with respect to the Ls→∞ limit needed to recover U(2), now under much better control. Auxiliary field ensembles generated on 163×24 with varying self-interaction strength g2 and bare mass m are used to measure the bilinear condensate order parameter ⟨ψ¯iγ3ψ⟩ with domain wall separations as large as Ls=120. The resulting Ls→∞ extrapolation is used to fit an empirical equation of state modeling spontaneous symmetry breaking as m→0. The fit is remarkably stable and compelling, with the fitted critical exponents βm≃2.4, δ≃1.3 differing markedly from previous estimates. The associated susceptibility exhibits a mass hierarchy in line with physical expectations, again unlike previous estimates. Schwinger-Dyson equation (SDE) solutions of the Thirring model exploiting a hidden local symmetry in the action are reviewed and analytic predictions presented for the exponents. In contrast to all previous lattice studies, the universal characteristics of the critical point revealed qualitatively resemble the SDE predictions. Published by the American Physical Society 2025