  A minimal model of a quantum refrigerator (QR), i.e. a periodically
phase-flipped two-level system permanently coupled to a finite-capacity bath
(cold bath) and an infinite heat dump (hot bath), is introduced and used to
investigate the cooling of the cold bath towards the absolute zero (T=0).
Remarkably, the temperature scaling of the cold-bath cooling rate reveals that
it does not vanish as T->0 for certain realistic quantized baths, e.g. phonons
in strongly disordered media (fractons) or quantized spin-waves in ferromagnets
(magnons). This result challenges Nernst's third-law formulation known as the
unattainability principle.
