Calculations of the superconducting critical temperature with vertex corrections

The calculations of the superconducting transition temperature, including the lowest-order vertex corrections, are carried out for three models: the BCS-type instantaneous interaction, a retarded isotropic interaction described by the Eliashberg spectral function α²F({Ω}) and a spin-fluctuation interaction with four {δ}-function peaks in the corners of a square Brillouin zone. In the isotropic case the effect of higher-order self-energy diagrams is to suppress the critical temperature calculated within the mean-field approximation when the characteristic energy of the boson responsible for the pairing is not small compared to the Fermi energy. In the case of the model with sharp peaks in the momentum space the vertex correction can lead to an increase of Tc.