  We use the epsilon expansion to explore a new universality class of second
order quantum phase transitions associated with a four-dimensional Yukawa field
theory coupled to a traceless Hermitean matrix scalar field. We argue that this
class includes four-fermi models in $2<D<4$ dimensions with $SU(N_F)\times
U(N)$ symmetry and a U(N) scalar, $SU(N_F)$ iso-vector 4-fermi coupling. The
epsilon expansion indicates that there is a second order phase transition for
$N\geq N^*(N_F)$, where $N^*(N_F)\simeq.27N_F$ if $N_F\to\infty$.
