Phase Diagram of High-T_c Superconductors from a Field Theory Model

The renormalization group approach to correlated fermions is used to determine the phase diagram of the oxide cuprates modeled by the t − t ′ Hubbard model at the Van Hove filling. Spin–dependent interactions give rise to instabilities corresponding to ferromagnetic, antiferromagnetic and d-wave superconducting phases. Antiferromagnetism and d-wave superconductivity arise from the same interactions, and compete in the same region of parameter space.