  The (2+1)-dimensional generalized massless Thirring model with 4-component
Fermi-fields is investigated by the Hartree-Fock method. The Lagrangian of this
model is constructed from two different four-fermion structures. One of them
takes into account the vector$\times$vector channel of fermion interaction with
coupling constant $G_v$, the other - the scalar$\times$scalar channel with
coupling $G_s$. At some relation between bare couplings $G_s$ and $G_v$, the
Hartree-Fock equation for self-energy of fermions can be renormalized, and
dynamical generation of the Dirac and Haldane fermion masses is possible. As a
result, phase portrait of the model consists of two nontrivial phases. In the
first one the chiral symmetry is spontaneously broken due to dynamical
appearing of the Dirac mass term, while in the second phase a spontaneous
breaking of the spatial parity $\mathcal P$ is induced by Haldane mass term. It
is shown that in the particular case of pure Thirring model, i.e. at $G_s=0$,
the ground state of the system is indeed a mixture of these phases. Moreover,
it was found that dynamical generation of fermion masses is possible for any
finite number of Fermi-fields.
