Proof of the nonexistence of formal phase transitions in polaron systems, exposed to a homogeneous magnetic field

Abstract

In the recent literature it was frequently claimed, that a polaron system, described by the parameters α (electron-phonon coupling), B (magnetic field) and T (temperature) should undergo a phase transition for certain values of (α, B, T). As usual, such a transition would lead to a discontinuity in the free energy F = F(α, B, T) or its derivatives. We prove that no such transition exists. F = F(α, B, T) is a real analytical function in α and B for all T (including T = 0). The shortcoming of all previous "proofs" is, that they all use variational procedures, which may cause artificial discontinuities. In fact, some authors have mentioned themselves, that their results are variational, so that the discontinuities which they encounter could be artifacts of their approximation. Our results can readily be transferred to the case of lower spatial dimensions. Further extensions to related systems like quantum well structures are possible.