Ferromagnetic Instability and Finite-Temperature Properties of Two-Dimensional Electron Systems with van Hove Singularities

We study a ferromagnetic tendency in the two-dimensional Hubbard model near van Hove filling by using a functional renormalization-group method. We compute temperature dependences of magnetic susceptibilities including incommensurate magnetism. In the phase diagram spanned by the chemical potential and temperature, the ferromagnetic tendency is found to occur in a dome-shaped region around van Hove filling with an asymmetric property: incommensurate magnetism is favored near the edge of the dome above van Hove filling whereas a first-order-like transition to the ferromagnetic ground state is expected below van Hove filling. The dome-shaped region in the phase diagram is well captured in the Stoner theory by invoking a smaller Coulomb interaction. Triplet p-wave superconductivity tends to develop at low temperatures inside the dome and extends more than the ferromagnetic region above van Hove filling.