Phase structure of the Schwinger model on the lattice with Wilson fermions in the Hartree-Fock approximation

The phase diagram of the Schwinger model on the lattice with one and two degenerate flavors of Wilson fermions is investigated in the Hartree-Fock approximation. In the case of a single flavor (not directly amenable to numerical simulation), the calculation indicates the existence of the parity-violating phase at both weak and intermediate-to-strong couplings. In the broken phase, the Hartree-Fock vacuum sustains a nonzero electric field. With two flavors, parity is not broken at weak coupling. However, both parity and flavor become spontaneously broken at the Hartree-Fock level as the coupling becomes strong. \textcopyright{} 1996 The American Physical Society.