SDW antiferromagnetic phase in the two-dimensional Hubbard model: Eliashberg approach

The two-dimensional Hubbard model was used for the description of the spin density wave (SDW) antiferromagnetic phase. The calculations were conducted in the framework of the Eliashberg formalism. The SDW phase that characterizes with the order parameter of the s-, extended s- or d-wave symmetry has been considered. The Eliashberg equations for the half-filled electron band have been constructed, with a use of which, it has been shown that only the SDW phase of the s-wave symmetry induces in the system. Next, the dependence of the s-wave SDW transition temperature on the value of the on-site Coulomb repulsion parameter was determined.