On the Existence of a Phase Transition for the Fröhlich Polaron

The ground state energy and its first and second derivative with respect to the electron‐phonon coupling are calculated for the polaron theories of Feynman, Lépine and Matz, Mańka, Pekar, and the Gaussian approximation. It is suggested that the phase transition, from the mobile to the localized polaron state, found by some authors is a feature of their approximation rather than an intrinsic property of the Fröhlich Hamiltonian.