Phase transition and critical behavior of d=3 chiral fermion models with left-right asymmetry

We investigate the critical behavior of three-dimensional relativistic fermion models with a U(N-L)(L) circle times U(1)(R) chiral symmetry reminiscent of the Higgs-Yukawa sector of the standard model of particle physics. We classify all possible four-fermion interaction terms and the corresponding discrete symmetries. For sufficiently strong correlations in a scalar parity-conserving channel, the system can undergo a second-order phase transition to a chiral-symmetry broken phase, which is a 3d analog of the electroweak phase transition. We determine the critical behavior of this phase transition in terms of the critical exponent nu and the fermion and scalar anomalous dimensions for N-L >= 1. Our models define new universality classes that can serve as prototypes for studies of strongly correlated chiral fermions.