Electrodynamics and thermodynamics of a paramagnetic system in a metallic resonator

The well-known problem of the phase transition in a two-level system coupled with the radiation field of a resonator is considered subject to the conduction electrons of the resonator walls. It is shown that the conduction electrons are important for consideration of the high-frequency properties of the system to cut off the frequency spectrum of the radiation field at the plasma frequency. In the vicinity of the phase transition the conduction electrons lead to the damping of the soft mode.