  We describe the transition from a ferromagnetic phase, to a disordered para-
magnetic phase, which occurs in one-dimensional Kondo lattice models with
partial conduction band filling. The transition is the quantum order-disorder
transition of the transverse-field Ising chain, and reflects double-exchange
ordered regions of localized spins being gradually destroyed as the coupling to
the conduction electrons is reduced. For incommensurate conduction band
filling, the low-energy properties of the localized spins near the transition
are dominated by anomalous ordered (disordered) regions of localized spins
which survive into the paramagnetic (ferromagnetic) phase. Many interesting
properties follow, including a diverging susceptibility for a finite range of
couplings into the paramagnetic phase. Our critical line equation, together
with numerically determined transition points, are used to determine the range
of the double-exchange interaction. Models we consider are the spin 1/2 Kondo
lattices with antiferromagnetic (Kondo) coupling, with ferromagnetic (Hund's
rule) coupling, and the Kondo lattice with repulsive interactions between the
conduction electrons.
