Low-temperature properties of the Hubbard model

Self-consistent equations corresponding to the single-loop approximation at an arbitrary relation between the Hubbard energy $U$ and hop integral $t$ have been obtained for the determination of the energy spectrum in the Hubbard model. The conditions of the insulator-metal transition, as well as the conditions for the transition from the paradielectric to antiferromagnetic state (spin-density wave), have been determined in the case of an exactly half-filled band.