New Universality Classes for Quantum Critical Behavior

Abstract

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 $N\ge N^{\ast }(N_F)$, where $N^{\ast }(N_F)\simeq .27N_F$ if $N_F\to \infty$.

Comments: LaTeX, 9 pages, 1 tarred and uuencoded postscript figure. The new version contains information on the asymptotic dependence of the critical number of fermion species on $N_F$