We study an asymptotically free theory of N relativistic Dirac fermions and
a real scalar field coupled by Yukawa and scalar self-interactions in three
dimensions using functional renormalisation. In the limit of many fermion
flavours, the cubic scalar coupling becomes exactly marginal due to quantum
fluctuations, leading to a line of strongly-coupled infrared fixed points.
Fermion mass can be generated through a quantum phase transition even if chiral
symmetry is absent. The line of fixed points terminates at a critical endpoint
due to the loss of vacuum stability. Exactly at the endpoint, scale symmetry is
broken spontaneously, leading to the generation of fermion mass. Intriguingly,
the absence of chiral symmetry is a prerequisite for the spontaneous generation
of fermion mass, and not a consequence thereof. We also highlight close
similarities between Gross-Neveu and Gross-Neveu--Yukawa theories at and away
from critical points, and establish the large-N equivalence of their
functional RG flows and quantum effective actions. Further implications
including for conformal field theories are indicated.Comment: 13 pages, 5 figure