Response functions, superconductivity and ferromagnetism in the many fermion system

Abstract

At the phase transition, the anomalies of thermodynamic and static response functions coincide due to the fact that the free energy, expressed in terms of response functions at imaginary frequency including zero, has its pole at zero frequency. Previous work has considered the singularities which arise from the polarisation of the medium. In this paper, a study is made of the divergences arising from the modification of the vertex function. The diamagnetic current is related to the free energy via the Ward Identity so that the specific heat anomaly inevitably gives rise to the Meissner effect. Below the transition the system adjusts to the singularity by going into the BCS condensed state. The similarity between BCS theory and ferromagnetism is shown both through a Weiss field approach and diagrammatically by including special correlations between k and - k. Its importance for an understanding of the broken symmetry problem is discussed. Finally, the parallel behaviour of the susceptibility and specific heat of a Bloch ferromagnet is demonstrated.