  Using a nonperturbative approach based on the Cornwall-Jackiw-Tomboulis
effective action $\Gamma(S)$ for composite operators ($S$ is the full fermion
propagator), the phase structure of the simplest massless (2 + 1)-dimensional
Gross-Neveu model is investigated. We have calculated $\Gamma(S)$ and its
stationary (or Dyson-Schwinger) equation in the first order of the bare
coupling constant $G$ and have shown that there exist a well-defined dependence
of $G\equiv G(\Lambda)$ on the cutoff parameter $\Lambda$, such that the
Dyson-Schwinger equation is renormalized. It has three different solutions for
fermion propagator $S$ corresponding to possible dynamical appearance of three
different mass terms in the model. One is a Hermitian, but two others are
non-Hermitian and $\cP\cT$ even or odd. It means that two phases with
spontaneous non-Hermiticity can be emerged in the system. Moreover, mass
spectrum of quasiparticles is real in these non-Hermitian and $\cP\cT$ even/odd
phases.
