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A theory is presented for a nonequilibrium phase transition in thetwo-dimensional Hubbard model coupled to electrodes. Nonequilibrium magneticand superconducting phase diagram is determined by the Keldysh method, wherethe electron correlation is treated in the fluctuation exchange approximation.The nonequilibrium distribution function in the presence of electroncorrelation is evoked to capture a general feature in the phase diagram.

Nonequilibrium magnetic and superconducting phases in the two-dimensional Hubbard model coupled to electrodes