Phase Transition of Fröhlich Polarons, in the Feynman Approximation, Subjected to a Magnetic Field

It is shown that the Fröhlich polaron in a magnetic field (calculated in the Feynman approximation) exhibits a first‐order phase transition if the electron‐phonon coupling constant α is larger than 4.2. For α = 4.2 the transition is of second order. The phase transition manifests itself as a discontinuity in the magnetization, the susceptibility, and the polaron mass for a critical value of the magnetic field. It is found that at the transition point the phonon cloud surrounding the polaron cannot follow the electron in its motion in the magnetic field.