  Non-equilibrium phase transitions are studied theoretically for the
two-dimensional Hubbard model subject to bias voltages from the electrodes
coupled to the system. By combining the fluctuation exchange approximation with
the Keldysh method for non-equilibrium, we have studied the properties of the
non-equilibrium Fermi liquid phase and determined the phase diagram with
transition to non-equilibrium magnetic and superconducting phases.
