Proof of the nonexistence of (formal) phase transitions in polaron systems. II

In recent literature it was frequently claimed that free polarons should undergo a (formal) phase transition from a mobile to a localized state, if the electron-phonon coupling parameter α exceeds some critical value ${\alpha }_c$. For α=${\alpha }_c$, the formal free energy should be nonanalytic in α. In this paper we prove that for nonoptical polarons no such transition exists for finite temperatures. Our results can be generalized to the case of lower spatial dimensions as well as to polarons in homogeneous electromagnetic fields. We include some comments on related problems; in particular, the partition function of an electron moving in a Gaussian random potential is considered.