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The (2+1)-dimensional generalized massless Thirring model with 4-componentFermi-fields is investigated by the Hartree-Fock method. The Lagrangian of thismodel is constructed from two different four-fermion structures. One of themtakes into account the vector$\times$vector channel of fermion interaction withcoupling constant $G_v$, the other - the scalar$\times$scalar channel withcoupling $G_s$. At some relation between bare couplings $G_s$ and $G_v$, theHartree-Fock equation for self-energy of fermions can be renormalized, anddynamical generation of the Dirac and Haldane fermion masses is possible. As aresult, phase portrait of the model consists of two nontrivial phases. In thefirst one the chiral symmetry is spontaneously broken due to dynamicalappearing of the Dirac mass term, while in the second phase a spontaneousbreaking of the spatial parity $\mathcal P$ is induced by Haldane mass term. Itis 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 anyfinite number of Fermi-fields.

Hartree-Fock approach to dynamical mass generation in the generalized (2+1)-dimensional Thirring model