  The magnetic excitations of the double exchange (DE) model are usually
discussed in terms of an equivalent ferromagnetic Heisenberg model. We argue
that this equivalence is valid only at a quasi--classical level -- both quantum
and thermal corrections to the magnetic properties of DE model differ from any
effective Heisenberg model because its spin excitations interact only
indirectly, through the exchange of charge fluctuations. To demonstrate this,
we perform a novel large S expansion for the coupled spin and charge degrees of
freedom of the DE model, aimed at projecting out all electrons not locally
aligned with core spins. We generalized the Holstein--Primakoff transformation
to the case when the length of the spin is by itself an operator, and
explicitly constructed new fermionic and bosonic operators to fourth order in
1/\sqrt{S}. This procedure removes all spin variables from the Hund coupling
term, and yields an effective Hamiltonian with an overall scale of electron
hopping, for which we evaluate corrections to the magnetic and electronic
properties in 1/S expansion to order O(1/S^2). We also consider the effect of a
direct superexchange antiferromagnetic interaction between core spins. We find
that the competition between ferromagnetic double exchange and an
antiferromagnetic superexchange provides a new example of an "order from
disorder" phenomenon -- when the two interactions are of comparable strength,
an intermediate spin configuration (either a canted or a spiral state) is
selected by quantum and/or thermal fluctuations.
