  We study relativistic fermions in three euclidean dimensions with four- and
six-fermion interactions of the Gross-Neveu type. In the limit of many fermion
flavors, and besides the isolated free fixed point, the theory displays a line
of interacting ultraviolet fixed points. At the endpoint of the critical line,
we establish that mass is generated through the spontaneous breaking of quantum
scale invariance. Curiously, broken parity symmetry is a prerequisite for the
spontaneous generation of mass rather than a consequence thereof. We also
calculate critical exponents and find that hyperscaling relations are violated.
Further similarities with critical scalar theories, and implications for
conformal field theories and higher spin theories are discussed.
