  The analytical zero-temperature phase diagram of the double exchange model
for classical background spins as a function of the carrier density and Hund's
coupling in the entire range of these parameters is presented. By constructing
a continuum field theory we explore the possibility of a continuous phase
transition from ferromagnetic state to a gently varying textured state. We find
such a transition in and below two dimensions and show that the emerging stable
state is a spin-spiral which survives the tendency towards phase separation
into commonly considered phases, and is also energetically favored to the
canted state, for low carrier density.
