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 constant 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 optical polarons no such transition exists for finite temperatures. To do so, we use functional-integration techniques and discuss perturbation theory in α to infinite order.

• Received 14 July 1986

DOI:https://doi.org/10.1103/PhysRevB.35.4291