  We study a mesoscopic ring with an in-line quantum dot threaded by an
Aharonov-Bohm flux. Zero-point fluctuations of the electromagnetic environment
capacitively coupled to the ring, with $\omega^s$ spectral density, can
suppress tunneling through the dot, resulting in a quantum phase transition
from an unpolarized to a polarized phase. We show that robust signatures of
such a transition can be found in the response of the persistent current in the
ring to the external flux as well as to the bias between the dot and the arm.
Particular attention is paid to the experimentally relevant cases of ohmic
($s=1$) and subohmic ($s=1/2$) noise.
