  Ordinary ice has a proton-disordered phase which is kinetically metastable,
unable to reach, spontaneously, the ferroelectric (FE) ground state at low
temperature where a residual Pauling entropy persists. Upon light doping with
KOH at low temperature, the transition to FE ice takes place, but its
microscopic mechanism still needs clarification. We introduce a lattice model
based on dipolar interactions plus a competing, frustrating term that enforces
the ice rule (IR). In the absence of IR-breaking defects, standard Monte Carlo
(MC) simulation leaves this ice model stuck in a state of disordered proton
ring configurations with the correct Pauling entropy. A replica exchange
accelerated MC sampling strategy succeeds, without open path moves, interfaces,
or off-lattice configurations, in equilibrating this defect-free ice, reaching
its low-temperature FE order through a well-defined first-order phase
transition. When proton vacancies mimicking the KOH impurities are planted into
the IR-conserving lattice, they enable standard MC simulation to work,
revealing the kinetics of evolution of ice from proton disorder to partial FE
order below the transition temperature. Replacing ordinary nucleation, each
impurity opens up a proton ring generating a linear string, an actual FE
hydrogen bond wire that expands with time. Reminiscent of those described for
spin ice, these impurity-induced strings are proposed to exist in doped water
ice too, where IRs are even stronger. The emerging mechanism yields a
dependence of the long-time FE order fraction upon dopant concentration, and
upon quenching temperature, that compares favorably with that known in
real-life KOH doped ice.
