Fixed-point structure and critical behavior of generalized Gross-Neveu models in 2+1 dimensions

The universal behavior of matter near points of continuous phase transitions is an intriguing phenomenon in condensed matter and statistical physics. At quantum critical points, the presence of gapless fermion degrees of freedom leads to new quantum universality classes without any classical analogues. Here, we discuss zero-temperature phase transitions between two-dimensional Dirac semimetals and long-range-ordered phases, in which spin and/or charge symmetries are spontaneously broken. These transitions are described by generalized Gross-Neveu models in 2+1 dimensions. We identify and classify fixed points of the renormalization group in the theory space spanned by a basis of short-range interactions compatible with the given symmetries, and we compute the corresponding quantum critical behaviors. Implications for the physics of interacting Dirac systems will be discussed as well.