  We investigate the UV fixed-point structure of the three-dimensional Thirring
model by means of the functional renormalization group (RG). We classify all
possible 4-fermi interactions compatible with the present chiral and discrete
symmetries and calculate the purely fermionic RG flow using a full basis of
fermionic four-point functions in the point-like limit. Our results show that
the UV complete (asymptotically safe) Thirring model lies in a two-dimensional
coupling plane which reduces to the conventional Thirring coupling only in the
strict large-Nf limit. In addition to the Thirring universality class which is
characterized by one relevant direction (also at finite Nf), two further
interacting fixed points occur which may define new universality classes of
second-order phase transitions also involving parity-broken phases. The
Nf-dependence of the Thirring fixed point sheds further light on the existence
of an Nf-controlled quantum phase transition above which chiral symmetry
remains unbroken for arbitrary large coupling, even though a definite answer
will require a direct computation of competing orders.
