Statistical properties of polarons in a magnetic field. II. Numerical results and discussion on the phase transition

A detailed numerical analysis is made of the analytic results presented in paper I. Numerical results are presented for the mass of the Feynman polaron, parallel ($M_{\parallel }$) and perpendicular ($M_{\perp }$) to the magnetic field, and for the following thermodynamic quantities: the magnetization, the susceptibility, the internal energy, the entropy, and the specific heat. Those quantities are studied for different values of the electron-phonon coupling ($\alpha$), temperature ($T$), and magnetic field strength ($\mathcal{H}$). We found that an ideal gas of polarons undergoes a phase transition. In the physical parameter space ($\frac{1}{\alpha },\frac{1}{\mathcal{H}},T$) the points of first-order phase transition define a two-dimensional surface which is circumscribed by a line of second-order phase transitions. At the transition point the polaron transforms in the direction perpendicular to the magnetic field, and with increasing magnetic field strength, from a polaron state ($M_{\parallel }\approx M_{\perp }$) to an almost free Landau state ($M_{\parallel }>>M_{\perp }\sim 1$). This transition can be viewed as a magnetic-field-induced two-dimensional stripping of the polaron. The experimental consequences of this phase transition on the thermodynamic quantities and the magneto-optical absorption spectrum are discussed.